I understand that perspective, but to me it seems a failure of history. If we had simply thrown out all of our previous knowledge when we discovered 'lower level' understandings and reformulated them in those terms, we would see no 'special values'. Those values would be 1. And all else would be derived from them, and the things at our scale would look complex and maddening. Temperature measured in Kelvin, velocity measured in ratios off the speed of light, distance based on the planck length, things like that (although I know you're talking more about the fine structure constant and things of that nature, but I think it could be done with them as well).
The question, in my mind at least, is how to show that the quantum understanding leads, on the macro scale, to the emergent phenomena we observe and once thought unitary. That's a great degree of precision and division between entities to arise out of the nonlinear interactions of bunches of 'particles'. And given the scale on which such things emerged (the universal one), clearly a proper system of understanding would make the emergence of things like atoms, molecules, chemistry, astronomy, geologies, planets, solar systems, galaxies, stars, and all those things self-evident. But... save for a few exceptions (more all the time though which is encouraging!) we rarely even look at things en-masse. It's all well and good to know how 2 bodies interact under gravitation. But when your system falls apart with 3, and you really need to be able to toss in a trillion with dozens of other nonlinear relationships... It really ought to be more obvious, I would think, that we're missing something.