Axioms

> Physical constants that carry units do not carry any physics. The universe does not care about the value of the speed of light.

The universe may not care about the speed of light, but the stuff in the universe surely does. To borrow from your "theoretical physics normalizes everything to 1" example, the mass of the proton is much, much (numerically) smaller than the charge of the proton, and surely there's some physical significance of that? Or, alternatively, we can say that there's nothing wrong with the proton, and instead it's gravity which is too weak, but that's just reframing the same question in different units. I'm not sure you can ask that question without using units at all.

Ultimately, I suppose the "proper" framing of this question is some nonsensically complicated question about why the relevant quantum fields happen to interfere in exactly the way that they do to give the proton the properties that it has. But you can't even ask that question until you know what gravity is, at a quantum level, and to the best of my knowledge, nobody does.