If a real/true singularity existed our models and theories would become useless to predict what would happen in that singularity.
For example if naked singularities really existed, we could not predict what would happen to the universe since laws would become useless to predict what would happen.
But cannot we know somehow, depending on the conditions or the theory (for example a different theory than General Relativity) in which the singularity would exist (for example depending on the degrees of freedom or the laws of the "place" where the singularity would exist) if a singularity would really break laws of physics (even the most fundamental ones and even invariances, leaving a universe with "no rules")? I mean although we couldn't exactly predict what would happen in the singularity with accuracy, couldn't we at least predict this somehow?
And another question: When physicist say that the fact that equations become "break" at the singularity does not mean that laws are broken or something similar, are they saying that although this could be possible, it does not necessarily mean that? I mean, "really breaking the laws" would be included in the range of possibilities that a singularity could do (although it would be really improbable)? To put a simple analogy: Would it be like getting number 6 when throwing a dice 1000 times in a row? I mean, it would be extremely improbable, but it could possibly happen; this result would be inside of the range of possibilities that could happen when throwing the dice 1000 times.
PD: I'm not asking for newly developed theories that try to handle singularities without their typical extreme conditions and because of that, can work even with the presence of a singularity