I’d be interested in seeing a source on that. My understanding was that it was a powerful and popular computational tool. The theory is approximate but approximate theories can still be quite useful if the approximation is a good one.
It's basically an open secret, no one really believes DFT has much predictive power in strongly correlated systems (where relevant electrons cannot be treated as independent). It's not useless, but DFT calculations require many arbitrary choices and are hardly "first principles" in a meaningful way.
The LBNL DFT paper isn't claiming to have modeled the strong correlations. Rather, they observe a specific feature of the band structure (flat bands crossing the Fermi level formed from d-orbitals) that have also appeared in DFT calculations of other high-temp superconductors and are considered a signature of those materials. In the other high-Tc materials, the calculations are consistent with experiment, and so the unexpected appearance of these bands in the reported crystal structure is seen as a signal of "hey, if this turns out to be real, we can explain it with current physics." That's something that previous fraudulent claims of room temperature ambient pressure superconductors (University of Rochester group) couldn't do.
The other interesting conclusion of the LBNL paper is that the low-energy physics of the electronic structure can be effectively modeled by a two-level effective Hamiltonian. This is a common pathway to bridging the gap between DFT calculations and theoretical understanding of strong correlations.
None of the serious scientists are saying "hey, look, DFT predicted it so it's true." Rather, it doesn't rule it out, and it suggests that it could be understood with our current physics. That's significant in itself.
From my understanding of DFT that makes sense but it seems like in that case you are using the wrong tool. Approximate theories are good when the approximations are good. If your phenomena is strongly correlated, throwing out those correlations is bad.
I have no idea if the use of DFT here is appropriate or not.
DFT is generally good for well characterized phenomenon. Superconductivity is a bit of an edge case, really dependent on quantum effects that you need ab-initio quantum mechanics simulations to predict.
