We have two competing theories. One says everyone has a soul, and the True Horcrux ritual lets it survive death. The other says normal people don't have souls, and the True Horcrux ritual creates one, which can then survive death.

I'm not convinced that the first theory isn't just as parsimonious. It models the soul as something that needs to be anchored to the world. The (original) living body is always an anchor, and the TH ritual creates more anchors.

This also reminds me of the fact Draco believed Muggles have no souls. I now assign a higher credence to that idea.