The FCCs primary concern is devices not interfering with each other. Part of that is cutting up areas geographically and by spectrum, so you know that the 100MHz FM station in one area won't over lap with another's and both can transmit. My guess would be that mobile transmitters are required to fill out paperwork about how they won't interfere anywhere in the US. I could be wrong though.

"Requires separate approvals" does not always mean that approval is hard to get. It might require a version of the dish that doesn't do something v1 or v1 and v2 current do however.

Movement shifts spectrum so theoretically it may require bigger guard bands and slightly different paperwork. OTOH, I doubt SpaceX allocated spectrum is tied to a any particular location (as opposed to say - within country bounds), considering it's satellite communication.

Starlink itself cares about positioning to avoid overcrowding and also any satellite tasking/scheduling/whatever.