> There are an infinite number of problems that require a unique proof

Yes. The problem isn't that there won't be any problems. The problem will be the rate of general progress and solutions that at least some awareness is required of, to reliably identify a good new unsolved problem will just keep getting more challenging. And then an attempt needs to be make, to solve it in a very short time.

There is always another race to run too, but increasingly slow runners don't find that translates to winning.

This change is not going to slow down, it is going to speed up. Machines will be doing math systematically, checking off the meta-math theorems that ensure axiom combinations are covered, that the search does not stop where theorems are not exhausted, and does stop where it can be proven they are. Humans will never operate at that level.