What is set theory useful for beyond the contents of arithmetic, algebra, calculus, etc...
Category theory is useful for studying mathematical structures in general — by its nature, it’s results are going to be fairly abstract and general, but that doesn’t make it useless.
There's no doubting the important role of category theory in modern mathematics. Less clear to me is why programmers seem so keen on learning category theory. I studied a fair amount of abstract algebra in grad school and never once have I found it useful in my day to day life as a programer. At best, I can say that if you've mastered category theory then you know how to think abstractly and modularize complicated concepts. But there are many less circuitous routes to obtaining those skills that don't involve understanding what a monad is. The moment I'm reading a programming tutorial that starts talking about monads and monoids is the moment I go read some other tutorial that actually teaches a useful skill.
Category theory is useful for studying mathematical structures in general — by its nature, it’s results are going to be fairly abstract and general, but that doesn’t make it useless.