I think it goes even deeper than that. The speed of light is assumed to be constant on the basis that any observer anywhere who measures electrical and magnetic properties of a vacuum will get the same numbers. E.g., the electric field due to a unit of electrical charge is the same here as it is halfway across the universe.
If those properties can change from place to place, then the speed of light can likewise change, and an observer can detect his motion through a vacuum by monitoring its value. Who's to say they don't change?
40 years ago when I got my degree in physics I asked those kinds of questions of my professors. They pointed out that there was an opportunity for me to make my mark in physics if I could answer those questions myself. Well, I didn't have the horsepower then, and got my degree anyway. But I still wonder.