The BCS theory does a reasonably good job of describing the properties of so called ‘conventional superconductors’ which are actually a very small class, dwarfed by the ‘unconventional superconductors’ which include almost everything high-Tc.

However, BCS is built upon a pile of questionable assumptions and simplifications and there are signs that it’s not even a good theory for describing conventional superconductors. I think of BCS as something of a ‘local maximum’ in the space of theories describing superconductors and we’re all stuck trying to find ways of incrementally improving the theory when really we’re going to have to make a large leap to a quite different description before real progress is made.

It’s like climbing a tree to get to the moon. You get a little closer, but to get any further you’re actually going to have to climb down and do a lot of work on earth before getting any higher.