I would say might turn out to be irrelevant to the real world. It depends on how the various proposed "no singularity" solutions for the early universe and for black holes (actually "apparent" black holes if the proposals work out, since the proposed solutions contain no event horizons, only apparent horizons) pan out. If they work out, then yes, it would be true that the singularity theorems only apply to solutions that turn out not to describe the real world--in the solutions that describe the real world, key assumptions that go into the singularity theorems are violated (mainly the energy conditions).

One could argue that an additional contribution of the singularity theorems is that it they frame how to think about the general problem of singularities ( not tied to a particular class of solutions ). If more cases are needed, then they may arise as variations of existing theorems... possibly with different ways of imposing conditions needed to complete the proofs.