Of course the proponents of these other foundations claim that they are suitable for universal use. But sets came first, and is good enough for most purposes, a

Of course the proponents of these other foundations claim that they are suitable for universal use. But sets came first, and is good enough for most purposes, and mathematicians in general are more concerned with mathematics than foundations. Actually the recent movement of "Homotopy Type Theory" is gaining some traction among non-logicians, giving easier formulations and proofs in category theory and topology. Also in computer science type theory is becoming more usual, since all results are constructive (provides algorithms) and is in fact a programming language in it self.