OK, you're mixing up a bunch of things, so lets take them one at a time.
I was wondering why hard cc's can't interrupt enemies?
It can. Stuns interupt channels all the time. Just ask any Nunu or Katarina player.
's cage is special in that it's the only stun that can interrupt dashes.
Every other time you want to interrupt a dash, you need a knockup.
if you stun lux or ezreal mid ult, their ult still goes off. It should go on a 1 second cooldown or something.
Ezreal and Lux's ultimates aren't channels. They're cast instantly, but they have a cast animation that takes a while to go. If you pull an Ezreal or Lux while they're winding up their ultimate, it still fires from the original position. If it was a channel, it would stop when you CCed them.
And I think when you hard cc someone, they shouldn't be able to be able to pull that last auto attack off and potentially kill you when they're stunned.
If they'd already started the animation for the auto attack, why shouldn't it go off?
Look at it the opposite way. If you're a mage, and you cast a spell (say a Ziggs ultimate) and someone silences you after the ultimate leaves your hand, should your ultimate just disappear? No, you already sent it on its way. Same thing with auto attacks.