I probably have been reiterating the same things for these questions! The thing is that singularities being resolved is an entirely different thing. Fuzzballs are real, but in the full landscape of general relativity, singularities are just fine. I doubt resolution of singularities would be that singularities in general can be "removed". You are right that they don't have to be just mathematical things to be resolved. Most of the people working with these things don't see them that way -- for that matter, singularities are good! See https://physics.stackexchange.com/a/781724/365939, since I think I detailed a nice aspect of singularities. Singularities being physical has always been accepted; and for that matter resolving singularities in holographic quantum gravity has a no-go principle. I am not sure what the end product of the whole program would be, but I for one don't think they would be resolved.
