Artifact weapons are going to be a major feature in Legion. While I'm pretty excited about them, I also realize some of the inherent problems. Consider, for example, if you're a Fire Mage who really likes some Firelands staff model and always uses it for transmog. That person is either going to be out of luck when it comes to using a staff for probably the next two years (or even longer, if they make good on Legion being an extra-long expansion.)
Artifacts are going to be a pretty different way for the game to work, and while I'm really happy that I never have to worry about having a shield that's crappier than my sword or vice versa, as both will be boosted by the same relics, I'm also sure that we'll be ready to strap on new weapons when we move on from the Broken Isles.
That said, it'll be really weird to replace the Ashbringer or the Doomhammer with some quest green.
Personally, I hope that every appearance for your artifact weapon gets unlocked in the appearances tab - historically they've restricted legendaries from being used for transmog, but A: artifacts aren't legendaries and B: they're starting to get flexible on that, with the Mists of Pandaria Legendary cloaks now available for transmog.
In fact, I wouldn't be shocked if in 8.0 we start to see all legendary weapons now valid for transmog, but we're nowhere near that.
The other consequence of dumping artifacts after Legion is that a lot of the balance of the game is built around artifact weapons - my Enhancement Shaman, for example, takes forever to build up Maelstrom right now, but when he picks up the Doomhammer, he'll have the one-minute cooldown Doom Winds, which will help to generate a ton of Maelstrom on-demand.
Obviously every expansion comes with serious balance changes, and there's no reason to think that Blizzard wouldn't be able to balance 8.0 with the absence of artifacts.
I do wonder, though, how quickly we'll be rid of them, unless the game forces us to ditch them in some artificial way. The many artifact traits give some serious boosts to our damage. Someone who levels up through the Broken Isles after Legion ends will probably not have the most super-powered artifact - they'll probably not have all the traits filled out and will be using green or blue-quality relics, and so they'll probably be able to ditch the thing if they get a big item level boost on whatever the first quest in 8.0 is.
But for people who play through the Legion expansion and have fully-filled out artifact traits and epic relics from the final raid, I think Blizzard is going to need to seriously ramp up the item levels of the rewards in the next expansion to get people to let go of these things before they start raiding that expansion's first tier.
But all of this is a ways off, so for now let's just be excited about picking up our own artifacts in two weeks.