I think certain champions need nerfs/modifications to their kits, but assassins on the whole are pretty ok.
Take away base damage on Zed's ult, give him maybe a .2% damage amp on abilities hit on that target like fizz' ult.
Take away Fizz W passive. Leave the active as a toggle that consistently drains mana for every hit.
Ekko's W should scale up in length as you rank it up. Super long stun at early levels is not fun to fight. Q should not apply a slow twice (or two stacks of his passive)
Yasuo's shield should not just flat out block any one ability as it stands now. Maybe flow should stop generating while he's in combat? Maybe the shield should be consumed if the ability does more damage than it protects against? I dunno, but a little tweak to him would be nice.
Give Talon some more power in his Q, maybe something extra with his bleed. If he hits them with it twice, maybe it should stack, not just refresh bleed timer.
Little tweaks here and there to the rest of the cast, and I think assassins would be fine.