Often, we don't know the applications of new math. For a long period of time we had "useless", "purely theoretical" mathematics that eventually turned into relativity and quantum mechanics.

Proofs are somewhat like legos. A bigger toolbox of them can only help in solving other, possibly practical, problems.

As far as the utility of a human being involved -- In a non-theoretical world where we don't have feline mathematicians, what is the point of these proofs if there is no cat which actually understands it? The cats can benefit from, for example, advances to optimziation algorithms that reduce costs for cat food delivery, of course.