Assassins can kill one carry effectively, only get things out of burst + penetration (so flat stats over utility) in build paths. There's always been a wary collusion in this game between assassins and "traditional mages"; mages need to be able to "one shot" carries but are also designed to nuke entire teams to bits. But no, assassins and mages do not effectively have the same role, although the best ones are expected to be able to achieve the same things.
There has been no time in league's history where single target damage vs aoe damage has been noticeably fair/balanced (and by virtue, there never will be; riot have just purposely kept AoE on the down low in favour of...) If I was to coin this meta as anything, I'd call it the "lock down meta" (shaped by Thresh, Vi, etc), where right now teams are balanced around exclusive in-game usages/roles (in other words roles aren't overlapped, you have engage, follow up engage, tower killer and boom boomers) and the sheer power of taking out one of the enemy [instantly] severely outweighs the drawn out fighting or capabilities of off-meta characters because teams usually cannot achieve any map objectives without "everything" available. Dre, you have not been around to see this game where hard aoe cc boom boom engages are the best thing since sliced bread, and if you have, you'd probably realise that those characters who can achieve that are still strong and fully capable of aoe boom boom, but they just do not have the power bell curves throughout the length of the game like ******** overloaded kit characters like Vi and Thresh do (relevant at every stage of the game and even when completely shut down are still able to achieve base requirements that win games)
Basically, there's enough counter play available to older characters and their play patterns at this point, but there's close to little/none in relation to the characters in the spot light. Locking down a target and having characters being able to freely blow their loads with safety and without much concern for positioning is a design problem (especially with the characters who are potent at this have negative counterplay and usually amazing laning phases/early pressure, middle phases and are still heavily useful or better in the late game). However, the moment we actually get more counterplay going for these new problems, you'll see the transition to different niches of casters. Or maybe we won't... riot are getting pretty bad at managing this game at this point.
I know this game will actually make sense to me again when a character like Ashe can actually compete. But I severely doubt she ever will be without completely nonsensical changes.