[2020] Will interrupted ults go on full/limited cooldown in Fault?

I played a ton of Paragon and nothing irritated me more than interrupting an ult(like Morigesh) to save someone just to have them immediately cast it again after they came out of the stun, or knock up and still get the kill anyway. In my opinion this should be a counter play, there should be a consequence for using an ability even if it's an ult with a long cast time in an unsafe location.