NP completeness kinda works around the uncertainty of PxNP (with x ∈ {⊆, ⊊}), because it defines some sort of "weak subset" of NP comprised of "pretty sure these problems are not in P[, because no one yet thought of a polynomial reduction to a problem in P]". The last part in brackets is the catch here; if we could show that it is not possible, then P!=NP would immediately follow, and NP completeness would become a largely pointless exercise.
NP completeness would still be of interest for particular algorithms because it would prove that those problems could not be solved in polynomial time. For instance, if factoring was shown to be NP complete, that would be a really useful result both for showing the security of algorithms like RSA as well as potentially disproving the extended Church-Turing thesis if quantum computers can be created.
