I've wondered about that: Why privilege that frame of reference? It seems more intuitive and easier to work with, but do we have a better reason than that?
In a rotating frame of reference, forces appear in the equations that are proportional to the distance from the center. They are the forces necessary to make an object which is stationary in a non-rotating frame go in a circle in the rotating frame. Those forces do not correspond to springs, gravitating bodies or any physical phenomenon, and are called "fictitious forces." Non-rotating frames of references make those forces go away, and that is why they're special.