A proof longer than the size of the universe is also pretty useless and probably not something we need to worry about.

Like i guess you are saying we couldn't really use such a machine to determine whether a certain conjecture just has a very long proof/disproof or is actually undecidable. Which sure, but umm i think that is the sort of problem most mathematicians would love to have.

The real reason non-deterministic turing machines can't help us is that they dont actually exist.