> and do not necessarily imply superconductivity, let alone high temperature superconductivity
That's true, but are there superconductors that do not have those flat bands?
If not then it wouldn't be evidence that it is superconducting but it would at least check one more expected property (based on the evidence obtained about superconductors so far).
> That's true, but are there superconductors that do not have those flat bands?
Yes, many. Most (all?) conventional superconductors. High-Tc iron arsenide superconductors discovered ~15 years ago. DFT (without including Hubbard "U" type corrections) for the cuprate high-Tc superconductors also doesn't indicate show flat bands.
Examples that do have flat bands (or similar physics) include the recently discovered twisted bilayer graphene (still very much actively studied), as well as (morally speaking at least) heavy-fermion superconductors (too many to list).
Superconductivity is a phase of matter than can arise in a variety of different ways depending on the details of the underlying physics. So at least when talking about the microscopic mechanism that stabilizes the superconducting state there isn't any single theory or one set of predictions/properties.
That's true, but are there superconductors that do not have those flat bands?
If not then it wouldn't be evidence that it is superconducting but it would at least check one more expected property (based on the evidence obtained about superconductors so far).