Yes but incompleteness refers to things that are true but can't be proven to be true. I think you're referring to the idea of prospective axioms which can be p

Yes but incompleteness refers to things that are true but can't be proven to be true. I think you're referring to the idea of prospective axioms which can be proven to be independent of existing axioms (notably the axiom of choice). This is another thing altogether. In the end, knowing enough about something to reduce it to axioms is only the start and not the end of understanding. P = NP wouldn't suddenly trivialize the problems so much as indicate that a polynomial time solution exists somewhere.