The FCCs mandate is to protect the airwaves from interference. Starlink uses shared bands. if the receivers move, tracking down interference is harder.
this is not really true relative to what OP said. there are fcc regulations for spectral leakage and such, but that's well known and means you can't transmit outside a service area. but that just means you're in another, adjacent service area. it has more to do with the spectral efficiency going down as you move from boresight, so they don't want a capacity loss. fcc has nothing to do with this decision.