Isn’t this redundant, though? The constant velocity for light in a vacuum comes directly from the laws of (classical) electromagnetism in the form of Maxwell’s equations. So “the laws of Physics are the same in all reference frames” implies “Maxwell’s equations are valid in all reference frames”, which in turn implies “the velocity of light in vacuum is the same in all reference frames”. That’s what I understood reading Einstein himself.

I think it’s much stronger that way. Otherwise we get to why light should be a special case, which is difficult to defend. The constant velocity of light (in vacuum) being an unavoidable consequence of the laws of Physics makes it much stronger.

> I prefer to start there and derive e.g. Lorentz factors than start with the mathy stuff.

That’s how Einstein himself explained it (with trains and stuff, but still) and it makes a lot of sense to me. Much more than the professor who did start with the Lorentz transform and then lost everyone after 20 minutes of maths.