SpaceX has to allocate bandwidth on the satellites to consumers. If consumers move, they will have overallocated bandwidth in some places, degrading network performance. They'll probably come out with a mobile product at a higher price point in the future.
Kind of doubtful that consumers moving their terminals around would be statistically significant compared to all the other factors that cause regional variations in aggregated bandwidth usage.
If it were offered as a mobile service it would be very attractive to people on the go so it would skew the number of mobile nodes higher than expected. I think base station discovery is another issue blocking mobile nodes from happening so an in between step could be to provide a way to easily move your base station and register it to a new cell.
