Comment by emil-lp

I'm not the OP, but we usually don't build large theories on conjectures unless we have strong reason to believe they are true, such as P \neq NP, RH, etc.

The resolution of UGC will lead to a new theory in approximation algorithms. Suddenly we can build on top of the results that previously said "unless UGC is false".

But you're right in that the first step is simply to remove that last sentence from all the theorems.