Is there a deeper meaning to "Consider the speed of light in the Andromeda galaxy" that I missed? The speed of light is known to be constant in every reference frame.
You can reformulate all of physics into your Earthly non-inertial reference frame. You can formulate all of physics into a reference frame in which you personally are always stationary! Nothing stops you from doing it, and the physics will work, as much as they ever do (i.e., we know something's wrong with our theories). To the extent that the result is a hideous monstrosity, well, such is my point. Pondering the nature of that hideous monstrosity is something I think worth doing, at least for a bit. Not to the extent of actually writing the equations, though. It brings clarity to why inertial reference frames are so important that we almost consider "inertial reference frame" to be a single atomic word, because non-inertial reference frames are in general not very useful. (In specific they can be.)
Running through this exercise with some honesty can give one a greater understanding of why our physics is framed the way it is, and why it is that while all sorts of reference frames are valid, "inertial" reference frames are still important on their own merits.