Which is where adding constraints to the mix could help?I agree
No - it does not require these specific geometries! And that's exactly the problem. ST can be formulated with any number of non-compactified or large dimensions.
Constraints produce emergent results from complex brews like the ST landscape. Constraints select some particular equilibrium outcome.
What would this look like in this case? It would demand some kind of interaction between dimensions. So the construction approach takes each dimension as a non-interacting direction. This is atomistic in that each dimension just is, and gets glued additively to make whatever is seen to exist.
But if there is interaction between dimensions, then we would expect a self-organisation into some more particular arrangement. There could be a development from a landscape of possibilities towards some minima that is the least energy conformation.