But in practice, the bulk axioms are chosen and retained because the inventor thinks they or their consequences have some mapping to reality. This mapping is tested through applying the resultant math to some field and getting predictive success. In this regard the bulk of axioms are the same as any other beliefs except they are not arbitrary beliefs, and they are useful or believed to have the potential of usefulness.
And part of the problem is merely semantic. The word "belief" differs from the term "axiom" in other critical ways: "belief" regularly involves a call to action and includes concept that do not go though any tests for consistency let alone predictive success. If one asks "what is the difference between an assumption and an axiom" there is a lot less excitement.
Most interesting, I think, is the idea that basic axioms should be different than assumptions at all. That they can be definitively decided or the part of reality they map to is real and can be found.
I do not see why we would necessarily have evolved the mental equipment to work out every law of nature. No other animal has that, and while we clearly have better mental capacity I can't see why we would have evolved _every_ mental capacity.