Raids and instances and crafting would remain, but as content for quests.
Gear would remain, in fact become even more important, as the primary method of character advancement. Think of it like this: you start out with your usual terrible starting gear. The mobs early on will be easy, but they will get steadily harder. So much harder that you'll either have to start grouping up for quests or... do some easier quests and get gear from those.
There would still be 'levels' of gear, so a blue from WC will be much weaker than a blue from BRD which is much weaker than one from Gundrak. However gear would be primarily from quests or crafting. Instances would exist only for either lore or as places for more challenging quests and resulting better gear.
The result would be that a person in greens would be pretty common, all blues would be rare, and you simply would not find many epics at all. Think of the number of quest epics, that's about it.
What's the point? Well first off, I've recently found that I just don't like raiding. It's a lot of time being told what to do and failing because other people failed (not a bash at them, just the odds are against them). I also love quests. In fact I think I might like leveling more than end-game content simply because it is so much more quest-based. At the level cap you raid or do heroics, at least until you outgear them and then move on to only raiding. Maybe you do dailies, but they're not really quests; more like homework or a job.
Quests are discovery and adventure and lore. You learn more about the world and possibly take on some challenges along the way. What's wrong with them? For the most part, they give pretty poor gear. But that's only relative to raids which are gigantic loot pinatas, except every instead of just getting spun once, you get spun every time you swing, and someone steals money out of your wallet while you're distracted. My point is that quest gear is only bad because other gear is better. Yes, I know that sounded really dumb and obvious, but it has a lot of truth to it. We'd like quest gear more if there wasn't such easy superior gear from raids and instances and we'd not complain about the quality of it because there would be nothing to compare it to, except other quest gear.
I won't pretend this is a breakaway from the loot hamster wheel of current WoW. It's not. However it makes the hamster wheel a lot more interesting and less painful.
8 minutes ago