There is a progression that you can go through if you want to simply queue for instances in Legion. You get to the level cap, run some normal-mode dungeons and do some World Quests, then queue for Heroics once you have the requisite item level. You run that for a bit and then you can do LFR. This is basically how things have been since Dragon Soul, and while it's a flawed system to be sure (what system isn't?) it has worked out ok.
But there is a lot of stuff that you cannot do if you just want to queue for things.
When the dungeons in Legion were announced, there was talk of a Suramar dungeon that later expanded into two (originally they were talking about "Suramar City" which became Court of Stars and "Suramar Palace," which became the Nighthold. They later started talking about "Suramar Catacombs," which is clearly the Arcway.)
Far later into the run-up to the expansion, it was announced that the two Suramar dungeons would actually by Mythic-only and require you to get to a certain point in the Suramar quests before you could run them (annoyingly, Engineers can't get their max-level goggle schematics unless they run Court of Stars - the only profession quest I know of that requires a Mythic dungeon.)
The definition of a "casual" player is a pretty subjective one, but I think that someone who queues for instances and doesn't do pre-made groups is a pretty clear one. That means that casual players will truly be missing out on these two dungeons, as well as the headliner for the current patch: the Return to Karazhan, which is not only a Mythic-only dungeon itself, but also requires you to run four Mythic dungeons to get in the door (I literally only have Cordana Felsong left in my attunement. She's really that tough.)
The thing I find funny about this is that it's almost the opposite of the mid-Cataclysm issue that led them to introduce the Raid Finder difficulty. Basically, people could run Zul'Aman and Zul'Gurub (they were hard, but you could queue for them,) and so for the better part of a year, WoW was basically those two dungeons (because they gave better gear than the other dungeons) for a lot of people who couldn't organize raids or whose guilds couldn't down bosses in those raids. Firelands was the last non-LFR raid, and I can tell you that we certainly didn't get much down there while it was current.
So the irony is that at this point, you can waltz into Emerald Nightmare and easily down all seven bosses on LFR, but getting a group for Return to Karazhan is significantly more difficult.
The ethos behind LFR was that players should be able to experience the whole game even if they weren't able to commit to a regular raiding schedule and work through it with a guild. With all these Mythic-only dungeons, it seems as if Blizzard is abandoning that ethos.
Is that a good thing or a bad thing? Personally I'm finding it a little frustrating, but I also think you could make the argument that locking some content behind these difficulties makes it a little more special. I took down Deathwing basically the day that the second half of Dragon Soul LFR came out, and it was strange to see the expansion's main villain go down so soon. Stepping into normal mode raids after having done the fights on LFR does, of course, lessen the feeling of discovery. Perhaps reaching the top of Icecrown Citadel after months of progression might have felt less epic if I had done it on LFR months earlier.
But I also think about how this limits things - I suspect that I'm rarely if ever going to be able to DPS through any of these dungeons, because my guild relies on me to tank. Don't get me wrong - I love tanking, which is why my top three characters right now are a Protection Paladin, Blood Death Knight, and Vengeance Demon Hunter. But there is now this rather large barrier to entry for new content Blizzard is clearly putting a lot of effort into. I'm very excited to take on the new Karazhan, but I honestly don't know how many weeks it will take to ensure not only that I'm attuned for the dungeon, but also that a solid group of guild members (who can't always be there for every dungeon run, and thus aren't all getting attuned at the same time) can be.
My hope for the future in Legion is that new dungeons will be introduced that are not strictly Mythic-only. I recognize how this reintroduces the problem of making old content irrelevant if a new dungeon gives better stuff than an old one, but as I've argued before, in the era of LFR, it's not as if players wouldn't have been able to experience content when it was new. Ironically, while people will easily be able to do Emerald Nightmare and have been doing it for weeks, it's things like the Arcway, Court of Stars, and Return to Karazhan that risk being ignored as new content comes in.