Wavefunction used in Derivation of Josephson Effect

In deriving the Josephson Effect, the ansatz wavefunction is given as $sqrt{n} exp{(idelta)}$ which leads to the Josephson Relations. It seems that this wavefunction is used because $<psi|psi>$ should give the particle density. My question then, is that this ansatz wavefunction doesn’t seem to be limited to superconductivity, so why can’t the derivation for the Josephson relations be used to ordinary metals divided by a thin insulating layer as well? Where does the superconductivity play in the Josephson Effect?