Hm, I am in fact familiar with that, but I'd never thought of it quite that way. To be honest, now that you mention it and now that I analyse my previous thought processes, I'd up until right now always thought of an original singularity as sort of a property of the universe (as if spacetime really did break down in it) instead of a property of a theory (or the lack thereof). Mind Projection Fallacy all the way there.
Yes, I did know both that singularities are a breakdown in the description of a particular physical event, and that a final theory should explain that sort of thing, but I'd never really connected the two pieces of knowledge together.
That is... great. Thank you :)