Why do physicists dislike naked singularities? Why do physicists consider the potential existence of Naked singularities as a serious problem?
It is not clear why physicists dislike naked singularities. Mathematically a singularity just means a point where mathematics is not well defined. Physically this just means that the theory we have been working with no longer makes sense, and that research is needed to find a theory which does make sense. I don't see why this should be an issue. Physics advances by finding solutions to such problems. Often it seems as though physicists reify singularities, as though they must exist as a prediction of general relativity, but this is not so (as @safesphere remarked in comments). Of course, it would be objectionable to predict the physical existence of something which is mathematically meaningless. But general relativity does no such thing. It simply says that a singularity places a boundary on what we can understand at the present time.