Mind you, the DFT calculation from the Griffin paper is not a proof of LK 99 being a superconductor in any way. What it showed is the (potential) formation of flat bands near the Fermi surface. Band dispersion is associated with the kinetic energy of the electrons, so materials with flat band at the Fermi surface is more susceptible to interaction effect (and strong interaction causes all sorts of nonintuitive quantum effects). I’m not a DFT expert in any sense, but from what I’ve heard, it is quite easy to “tune” your model to produce narrow (the limit of which being flat) bands from substitutions (e.g. the Cu substitution in this case) and such, which don’t necessarily lead to superconductivity.

So I’ll take the DFT papers (there are quite a few now) as saying, “hey you want some flat band? Here’s some. We’ve done our part. Now some other theorist, do your magic and conjure up some superconductivity”. It’s a cog in the full picture, if there is a full picture