Invalidity of the BCS theory of superconductivity

A theory that purports to describe the natural world can be proven invalid by either (a) an experimental result or (b) a theoretical proof that it is internally inconsistent. However BCS is special: it cannot be disproved by (a) because any superconductor yielding an experimental result that doesn't conform to BCS is simply declared to be 'unconventional'. Hence we are left with (b). In a process where the temperature of a type I superconductor in a magnetic field changes, the London penetration depth and hence the magnetic flux changes, generating a Faraday electric field. BCS theory predicts that the electric field gives rise to a normal current and as a consequence Joule heat is dissipated, in an amount that depends on the speed of the process, and it also predicts that the final state is independent of the speed of the process. I show that these two predictions cannot be simultaneously reconciled with the laws of thermodynamics. Therefore, BCS theory is internally inconsistent. I propose a resolution of this conundrum through physics that is not part of BCS theory.