When you first start playing in Legion, I really do recommend sticking to one artifact (and therefore spec) for a while. Tanks at least are fine for leveling (I'm bringing up my Brewmaster at the moment, which is only slowing down because I've probably leveled up too many characters in too small a space of time and I'm just not feeling motivated to do Azsuna, which is his last zone to get through,) and I get the impression that healers can also put out enough damage to solo with reasonable efficiency (Paladins get a nice big hammer to smash people with, for one thing.)
Starting really with my Demon Hunter, who I began convinced he'd stick with Havoc, then wound up leveling him as Vengeance, and now have switched back to Havoc, I began to play with the idea of putting artifact power into an off-spec. Since then I've managed to get my Death Knight's Unholy artifact almost as powerful as his Blood one (and I'm even starting to toss some to Frost.)
And it's here that I think I'm beginning to see the cleverness of the artifact power and artifact knowledge system.
There's no cap on acquiring artifact power. If you ground endlessly, you could, in theory, eventually fill out your artifact with the only time limit being how long it takes you to clear random heroics.
The thing is, Blizzard doesn't want people to just get their artifacts fully powered immediately, but putting a cap on power acquisition wouldn't really feel good - you'd have people just hit their cap and stop playing for the week. They want the process to be a long-term progression, and so they make it so that each trait costs an exponentially higher amount (it might not be a strictly smooth exponential curve, but, you know, roughly.)
Artifact knowledge then lets them smooth out that exponential climb into something, if not linear, then at least shallower. At this point on my main, I get 650% additional AP from items I get, and so while I'm facing my next trait costing over 60,000 artifact power, it's a little less daunting when there are world quests giving me 3,000 AP from a single item.
The other really big thing is that if you want to start working on another artifact, you catch up, or at least get close to catching up, very quickly. As I said, I've focused primarily on Blood for my Death Knight. A little later, I started putting some into my Unholy artifact (so far I've been doing LFR as Unholy and dungeons as Blood, and mixing it up while soloing.) It went pretty quickly. Then, the other day, I did some quests in Suramar (he's still got a ways to go to finish that chain - I've only fully completed the zone's 7.0 content on my main) and with only two (admittedly bigger than usual) AP items, I managed to get 9 traits on the Frost artifact.
The point being: right now, if you've been playing since the expansion's launch and at a decent clip, you're probably at a point where your main spec's artifact is getting traits at a snail's pace. When you're looking at 60,000 artifact power to get the next trait, an item that gives you 1,000 isn't really going to blow you away. But if you have another spec that you've been ignoring, that item will get you I believe three traits right off the bat.
The system works pretty well, but I think there's only one potential flaw, which is that artifact knowledge requires resources and a lot of time. There is a slight catch-up mechanic, which is that the farther it's gotten from the expansion's launch, the more of a head start on research you'll get - you might start your research and see that it's immediately a third of the way to being done.
That's a good start, but I wonder if a year from now that means that the first few levels of artifact knowledge are going to have to be basically instantaneous. And given that the order resource cost for this research doesn't change, it will put a heavy burden on newer characters to gather tons of the stuff.
Blizzard has said that they're aware that they might need a more robust catch-up mechanic later on in the expansion's lifecycle, but I imagine we won't be seeing that until a later patch (and not 7.1)
Anyway, sacrificing a bit of AP for an off-spec is not going to set you back too far on your main spec, especially the farther you've gotten along on that main artifact. I'd also recommend getting any relic you can to fill out each slot in your off-specs, as even a 780 green (the highest BoE relic that drops randomly off anything, I believe) is better than nothing.