The problem with straight up assassin champs in LoL is solo q.
It's hard enough to get people to group as 5... let alone actually deal with countering an assassin. Usually what ends up happening is the team takes the assassin one at a time and gets wiped.
One guy gets caught out... deleted. Another guy is nearby and thinks he can help... deleted. The remaining 3 players all rush in to try and do something.... the opposing team comes in and CC's them... assassin then proceeds to delete, delete, delete. GG.
It's not about Katarina's ult at all. She doesn't even need it if she gets a couple levels ahead of everyone.
While I understand that fed champs are a problem in general... fed assassin's are the biggest problem.
You ever see a fed Master Yi? Yeah, that game is over in solo q. I've watched a Yi literally dive people under turret no problem and barely even take a scratch of damage. He's basically impossible to outrun once he is fed... so he just runs all over the place picking off people until the team surrenders. Something just needs to be done about these snowball champs that can fight through the entire team without a care. Like... limit their resources or something so they can only kill 1-2 people like that before they have to slow down and actually be cautious about continuing.
But right now it's like "YAY I GOT A KILL. NO STOPPING ME NOW! WEEEEEEEE!!!!" and then you just faceroll the keyboard until you get an ace.