Let's talk about the two games I'm currently playing in.
The one that has played far more consistently is set in Exandria. I'm playing a young Triton wizard who, fearing he was too meek and overhearing his beloved step-grandfather describing him that way, ran away with a magic, sentient book that used to be a powerful human archmage in the Age of Arcanum, technically stealing the book from the Cobalt Soul. Vodalos, the wizard, rolled pretty damn well on stats. I got a 17 and a 16, and so, using Tasha's rules to reassign his Triton ability score increases (and since then converting to the updated version of the race from Monsters of the Multiverse) he started off at +4 to Intelligence, +3 to Constitution, +2 to Dexterity and Charisma, +1 to Strength, and -1 to Wisdom (while my metagamey instincts think dumping Wisdom is a terrible idea, I wanted to reflect his naiveté and lack of worldliness - I also almost never roll insight against NPCs.)
The other game I'm in is a Spelljammer campaign - we've only had a handful of sessions in several months, so we're not even level 3 yet. But in this, I play a somewhat gruff artificer who works at the spaceport at Leira Trading Center (a city on the dark side of Toril's moon). By contrast, our DM had us use deterministic ability scores - we could do either point buy or standard array (I used point buy but just wound up with the standard array anyway,) so he's started off with +3 to Int, +2 to Dex and Con, +1 to Wisdom, +0 to Strength, and -1 to Charisma.
So, which way is better?
On my Wizard, it's been very freeing. We're level 4 at this point, and so he's got 20 Intelligence. With that squared away, I'm planning on taking Resilient: Constitution at level 8 - this will give him a +4 to Con and probably free up any future ASIs (at level 12, 16, and 19, should we get there) for feats, as I think +4 is probably plenty of Constitution for a ranged character.
However, there's also an element to it that doesn't feel quite fair - the party has two paladins, who each rolled poorly. We do have a house rule that if your rolled stats are worse than the standard array, you can just take the standard array instead, but this means that these two characters are forced to balance strength, charisma, and constitution (the tiefling seems to have taken the standard racial bonus, and then took Tavern Brawler at level 4, so they still only have a +2 to Strength). Thus, sometimes when I talk about the fun feats I'll take when we get into higher levels, I sometimes get a bit of wistfulness from other party members.
By contrast, while the Spelljammer campaign has barely gotten off the ground so far (we're supposed to play tonight, but I think the last three or four sessions have been canceled day of, so I'm trying to manage expectations) everyone is starting from the same point. The only reason I have a feat is that I'm the variant human in the party - we have two astral elves, a rock gnome, and a plasmoid. But I'm likely to just stick to ASIs as we level up - as I plan on being the group tank, I'm going to want to get my Intelligence and Constitution maxed out, which I could do by level 19. (Though I've been toying with the idea of instead making an Amulet of Health at level 14 and just grabbing feats at levels 12, 16, and 19, which would probably include Tough to make up for the lack of HP - only downside being that I'd be using up one of my infusions).
See, I think feats are more fun than ASIs, but I also have a sort of OCD compulsion to try to get at least my primary stats raised to 20.
As I often do, I'll compare this to the way that Starfinder does feats - it's the only other major, complex, class-based RPG I have the rules for. In Starfinder, feats are ubiquitous. Everyone gets a feat every other level, and several class features grant you feats. Whereas in 5th Edition D&D feats are an optional rule, in Starfinder they're pretty central to the game.
To be fair, though, some feats in Starfinder are very basic elements of the game. For example, every class in that gets a feat that lets them add their level to damage they do in any of the weapons the class is proficient in (numbers in Starfinder get a lot higher than in D&D - having an AC in the 30s is not that unusual). The action economy in Starfinder works quite differently, but you could imagine this as turning any feature that multiple classes get into a feat - essentially, it would be like making it so that all Barbarians, Fighters, Monks, Rangers, and Paladins would get the "Extra Attack" feat at level 5, rather than simply making those class features. It does open it up to other classes if they wanted to pick up the feature, though - so your Spores Druid might pick it up so that they could really focus on dealing poison damage with their Shillelagh.
Anyway, the reason I bring up feats is that I think that in D&D, it's a lot easier to consider feats if you roll high stats - because you're trading ASIs to get feats, you'll naturally feel a lot better about spending them if your main stat is already at 20.
With the Standard Array or Point Buy, you can't get any stat higher than 17 (+3) at level 1, which includes your racial (or really now "starting") ability score bonuses, which means that you'll need to spend at least two ASIs if you want to max it out. To get two of these maxed out, you'll need to spend three (or two if you used Point Buy to get two 15s at a severe cost to the rest of your ability scores).
That means five ASIs, which is all of them unless you're a Fighter or Rogue.
So, rolling stats, with the potential to get much higher, makes it less punishing to take feats. But it also creates inequality at the table.
Lots of people have come up with alternate ways to roll stats - adding flat amounts to a 2d6 roll, just simply rolling 3d6 (which is going to generally be lower than what you get in the PHB method,) or the like. But for the purposes of this, I'm going to instead look at a way to make this fair for the whole group.
On Critical Role, the rule they apparently use is that if you roll stats and you get less than a total of 70, you can re-roll. This means that your average ability score should be 11 2/3 or higher. This does ensure that no one gets totally screwed, but it's not going to do better than the standard array, and there's still potential for inequality. Indeed, while you might have a very well-rounded character, if you have 13s in all your ability scores, that's still going to mean a lot of catch-up on the stats that matter most to you.
Ideally, I'd want all the players to have the same average score.
Now, one way to do this is to give players a sort of point buy system, but change the way that the points work and how many they get. In D&D, point buy has diminishing returns for point investment - you need more points to get a higher score. This pushes players to have a more evenly distributed set of scores. But again, if we look at Starfinder, things are done a little differently.
There, I believe everything starts at 10 (though most races have negative score adjustments) and then you spend points in a linear fashion - if you're an android (who gets +2 to Dexterity) and you want to max out your Dex, you can put six more points in with the racial bonus to get to 18. In Starfinder, 18 is the highest you can start any stat out with, but it's actually very useful to start with something at 18 because later ASIs slow down starting at 17. (Like in D&D, the modifier is determined in the same way).
So, let's take the Standard Array and imagine this done in a linear fashion. 15, 14, 13, 12, 10, and 8 translates to a total of 12 points to spend - with the ability to gain up to two extra points by taking a negative 2 to one of your abilities. If we were to say we cap out what you can get with a single stat to 18, that would allow us to make, say, a Barbarian with 18 Strength and 14 Con and 10s in everything else. Or maybe we would take a -2 to Int and get 12 Dexterity.
If we then take our free +2 and +1, we could get a full 20 in Strength from the word go, and maybe give ourselves the +1 to Con so that we can get a +3 at level 4.
Clearly, some classes are going to have an easier time than others. If you're a Rogue, Sorcerer, or Wizard, you can probably stand to just max out your primary stat and then get some decent Constitution and leave most things at 10.
But, then, that's true of any of these systems.
Essentially, this system should allow you to re-create the Standard array, but it makes things more flexible if you want to specialize in certain abilities, at the cost of being less powerful in others. It will also allow a player who is willing to start with +3s to, for example, go for 15s in three stats (say, a Paladin with Strength, Con, and Charisma) and then use the racial/starting bonuses to put those to 16, with three left over to, say, make Strength 18 (or take a minus to something like Intelligence so they can get 18 in Charisma or Constitution as well).
If you want things a bit more randomized, but still fair, you could also do the following:
Everyone in the party rolls stats. Then, you simply take the best stats (determined by who rolls the highest total) and give everyone those values. Alternatively, you could take a hybrid approach to these two methods: everyone rolls, and you see who rolled the highest total. Then, you determine how many flat points that would be and everyone can spend those points as they wish. For example, my Paladin in Curse of Strahd rolled a 10, 7, 10, 17, 16, and 14, meaning she got to start with +4 to Strength and +3 to both Charisma and Constitution (with Scourge Aasimar bonuses). So, this would total out to 14 points to spend. A Rogue might then give themselves 18 in Dexterity and then 14 in Constitution and Wisdom while taking a -2 to, say, Strength (and then maybe max out Dex at level 1 with a +2 and then take +1 to Wisdom so they can grab observant and have amazing passive Perception at level 4). A Ranger could go for 16 Dexterity and 16 Constitution, and then 14 Wisdom, and maybe take a starting bonus of +2 to Wisdom and +1 to Dexterity, perhaps taking Gunner at level 4.
This gives the players the excitement of potentially having highly powerful characters, but doesn't leave anyone behind. And much as the 4d6 drop the lower skews things more powerful than the old school 3d6, but you'll also be selecting the very luckiest roller in the group to set the standard. Of course, this does mean the DM is potentially going to need to throw tougher fights at the party, but they can potentially balance things around that.
Now, this is all operating on the assumption that we want players to feel like they can take feats and have the chance to max out their ability scores. That sort of implies that we think that 5th Edition D&D characters are not powerful enough, which... I don't think is true.
So, there's another change we could make that makes feats more attractive by, instead, making ASIs less appealing.
Again, we're going to borrow an idea from Pathfinder. In Pathfinder, you get ability score improvements at levels 5, 10, 15, and 20. But rather than just raising one score by 2 or two by 1, you actually get to raise several scores at once. The key, though, is that if a score is 16 or lower, you get to increase it by 2 (unless it's 15... I don't have the book with me right now). Increasing a score beyond that point, you only raise the score by 1.
The result is that characters will naturally be more well-rounded, with plenty of decent scores, while raising a score to exceptional levels is much harder.
In D&D, we could implement a rule instead where once an ability score is 16, an ASI will only increase it by 1. Thus, to max out a score, you would need to put four full ASIs into it (or I guess 3 if you start with a 17). We'd also, naturally, remove the +1 to ability scores from feats that give those, or perhaps have them only grant that bonus if your score is lower than 16.
Thus, feats by comparison become a lot more appealing. Rather than rawly increasing the modifiers of our rolls, we're now getting more nuanced abilities. We might have a harder time succeeding on a Stealth check, but we might then consider something like Skulker to make those successes more impactful.
Feats are one of those "optional" rules that I've never seen anyone not use, but I also understand how they can make character builds that much more complicated. I'm very curious to see how they're treated in the 2024 PHB - given what we're seeing around the Giant UA and the revised Heroes of Krynn one, I think we might see them implemented as something to make character backgrounds a more impactful decision at character creation.