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.