Math is also useful. If someone showed that p = np tomorrow in a formally verified proof I don't care if no one can understand it.
A proof by contradiction that p = np is of no use to anyone, given that it wouldn't help you find any polynomial time algorithms for np-hard problems.
How would the mere knowledge that it holds, without any understanding why, be useful?
If a magic oracle tells you p=np, that's useless. How would that change anything?