The issue in that paper isn't really limited to "singularities". The basic issue is that we use the continuum in our physical models, and "reality" might not ac

The issue in that paper isn't really limited to "singularities". The basic issue is that we use the continuum in our physical models, and "reality" might not actually be a continuum, so the continuum math we use is just an approximation. But if "reality" isn't a continuum, it isn't a continuum everywhere, not just near "singularities", so the continuum is an approximation everywhere, not just near "singularities". The approximation would just become unworkable near "singularities", while remaining workable in other regimes. Most physicists believe that our best current theories, GR and quantum field theory, are approximations anyway ("effective theories" is the term often used in the literature), so that in itself is not a new idea. Baez's paper points at one fairly common hypothesis for why they are approximations and what the underlying theory they are approximations to might look like. I don't have an issue with that as a hypothesis; it's just something we aren't going to be able to test by experiment any time soon, since the most likely scale for where the approximation will break down, the Planck scale, is some twenty orders of magnitude away from the scales we can currently probe with experiments.