tl;dr - Shit's just to fast now, not just assassin burst, and it's causing the game to appear less balanced
Honestly i feel it's not that assassins aren't fun or lack counter play. It's that burst damage lacks counter play. It's the same reason that everyone still pretty much goes Thunderlords. Burst damage reduces the time you have to react to the champion.
Tank meta is fine, if the tanks were just these big brick walls, all defense and no offense, but because of how useless people felt as tanks in the previous meta where if you couldn't out burst the assassin's burst (after resistances), then you'd still just get slaughtered by them.
Really i think that one of the major causes of constant complaints about some champions being broken or not, stems from how fast the game has become, on a macro and micro scale.
Macro wise, a lot of games are now decided by 20 minutes at most ranks, because it takes a decent amount of coordination to recover from a 6k gold spread. It's not nearly as bad as it was in pre-season, but they are still way faster. The client still reads 30-45minutes, but realistically it's dropped down to 20-35 minutes (only because ff at 20).
In terms of micro play, a full rotation from most champions is enough to pretty much kill a single enemy given a slight lead in stats. Where as it use to be that you'd have maybe 2 or 3 skirmishes of full rotations, before going for the jugular or "advancing in the direction of your fountain".
Then some of the champions massively shifted the meta and overall design due to how they really don't have "rotations" rather they just have insanely short CDs, allowing them to simply tempo out their enemy when needed. looking at you
and now 