My personal take is that 3+1 is not privileged; but that the physics that takes place in the other combinations is either so uninteresting it doesn't meaningful

My personal take is that 3+1 is not privileged; but that the physics that takes place in the other combinations is either so uninteresting it doesn't meaningfully interact, or that the number of Feynman paths through the non-3+1 cases all (mostly?) cancel out.