I believe you're mistaken. There is value in axioms and axiomatic proofs: two different people will most definitively have a different notion of "obvious", and even have a different understanding of a mathematical problem. So a proof may be accepted by one person and rejected by another.
Given a set of axioms and proofs it's possible to mechanically check a proof. It's not quite possible to reliably check proofs otherwise.
Given a set of axioms and proofs it's possible to mechanically check a proof. It's not quite possible to reliably check proofs otherwise.