You have a few misconceptions and you are waaaaay overthinking this. The primary measure for this equilibrium is the time derivative of the mass-density-velocit

You have a few misconceptions and you are waaaaay overthinking this. The primary measure for this equilibrium is the time derivative of the mass-density-velocity, or momentum-density if you like. Now imagine a cube spinning on a primary axis. Since a cube is not constant radius, there are times where matter exists at a given point and other times where the matter does not exist at that point. Clearly, the time derivative of the momentum-density is not zero. This is not the case for a sphere as any point that has mass under the spinning sphere will have mass at all later points in time. The reason we don't just say sphere, though, is this kind of equilibrium accounts for oblate objects as well, and many planets are oblate.