Many consider naked singularities as a fundamental problem and that it should be always covered by a horizon (Cosmic censorship hypothesis). But why naked singularities are really a problem?
If we consider electrodynamics and the Coulomb potential, we have a singularity at $r=0$ but quantum electrodynamics solves the problem. General relativity being a classical theory we have also a singularity and with the hope that quantum gravity will remove it. But we don't need necessarily a horizon.
At classical level, naked singularities should not scare us. Why are they always disregarded?
Edit after the answer by John Rennie:
Thanks John Rennie for your answer. But we actually express exactly the same thing. I'm not saying that a singularity is not a problem, of course it is. But that singularity is not a problem within a classical theory because we expect or hope that the problem will be solved in the quantum regime.
Going back to my previous example, classical electrodynamics, no-one tries to hide a singularity behind a horizon but in general relativity we try to solve the singularity problem within the classical theory. The "Cosmic censorship hypothesis" tries to "solve" (most exactly hide) the problem within the classical regime.
My question then is, why not thinking that a naked singularity is a fair solution in the classical theory but the singularity would disappear in the quantum regime without necessarily imposing a horizon in the classical theory.