I am thinking something which could be similar as Gödel's works - but not with axioms of logical systems, but with symmetries of (theoretical) physical systems.
Such a proof would mean, that adding any new symmetry, would either contradict the others, or it could be derived from them.
I think, having such a proof would mean, that a theory is "ready". For example, I think the Newtonian Mechanics and the SR are probably "ready" in this sense, but I can't proove it.
Furthermore, applying the Noether theorem, it would also mean, that all conserved quantities of a theory were already found.