Math is also used to make a statement/model our universe. And we are still trying to find the theory to unify quantum mechanics and gravity. What if our math is simply inconsistent hence the theory of everything is not possible within the current mathematical framework?
Sure when you are solving the problems it is useless to ponder about it, but it serves as a reminder to also search for other ideas and not outright dismiss any strange new concept for a mathematical system. Or more generally, any logical system that follows a set of axioms. Just look at the history of mathematics itself. How many years before people start to accept that yes imaginary numbers are a thing.
Dunno what you’re trying to say. Yes, if ZFC is inconsistent it would be an issue, but in the unlikely event this is discovered, it would be overwhelmingly probable that a similar set of axioms could be used in a way which is transparent to the vast majority of mathematics. Incompleteness is more likely and less of an issue.
