Picked Anivia, against Zed
Level 2, q him while he aas minion, into e aa. Half his hp. He chugs a potion, I do it again, drop ignite and he dies.
Next, he gets 6. Ults me, landing 2 aas, 2 qs, ignite, and e. Very barely pops my passive, I only die due to xin coming in.
Level 9, he ults. He doesn't land q, uses ignite. Believe it or not, he _didn't actually deal 200% of my hp._
Yes, if he manages to weq you, he will do 50% of your hp.
So will literally every viable mid in the game, typically a lot easier than he can.
(Edit, I'm adding a bunch of additional examples, as one game probably isn't the best sample size.)
Cass vs Irelia, she never managed to solo kill me. Every time she would engage, I would dodge E, and she would either back off or dash in recklessly, I would q and kite, dealing a ton of damage with E. Considering Cass is counted as "Late Game" past levels 1/2, it wasn't exactly like I had a huge advantage on her. I even managed to solokill her at 6 with my ult. We did lose that game, but it had nothing to do with the mid laner.
Ahri vs Akali, she never managed to kill me. Literally just by _not standing in the shroud_, it was really difficult to die. Plus, one lucky charm and she was essentially dead. Very very few assassins have abilities which are _land and they die_, of course they do have their target access, but a good wall flash will save you. There are plenty of games where the opposite happened; Cass vs Ekko, I was doing perfectly fine until he got protobelt. From that point on, he could 100-20 me consistently, forcing me to farm under turret and play super passive until I got jungle ganks. It does all depend on player skill, champions, etc, but it isn't like assassins are so broken that it's not viable to play mages.