I remember blowing through proofs in a few seconds in Geometry class, so perhaps it might be so. Yet I can still hang my hat on what "useful" means, and thereby not eat it.
Arithmetic without X and / is not too useful. And pythagoreus was stumped by irrational numbers -- a suggestion that euclidean geometry -- in that clasical grade school "proof" context -- stops being useful at some point.
Note that in Pressburger arithmetic, you can multiply by any arbitrary integer, just not all integers.
Catagorical means that the axioms uniquely define the system up to isomorphisms.
Proofs of theorems are useful in keeping one from wasting time trying to compute the impossible. They also guide one into what might be interesting. (I've made a living by converting theorems into programs.)