AFAIK, most mainstream physicists assume the singularities are an artifact of the incompleteness of General Relativity, and that they won't exist in a theory of

AFAIK, most mainstream physicists assume the singularities are an artifact of the incompleteness of General Relativity, and that they won't exist in a theory of Quantum Gravity. Singularities and infinities in physics tend to indicate problems with a theory, they're the reason it's common to say that physics "breaks down" inside black holes.