So why did Shaco have to be nerfed into oblivion for URF but Zed still remains far more oppressive?

Shaco has CC and untargetability.

Same with how Teemo used to be disabled/heavily gimped in URF.

Shaco AoE fear that makes it near impossible to do anything into him if you don't immediately get sweeper.

Zeds ult can be completely nullified with 2900g, which is pretty darn easy to obtain in URF. Without ult to burst, he's just a really annoying mobile poke heavy champion (if your teammates don't randomly feed him in lane)