I understand your thinking, but that doesn't seem to be the vibe in Tampa right now. That said, I'm a little surprised the family didn't make arrangements for the kid to finish out the school semester and the football season - living with another family, if necessary (which I believe would be OK since Jesuit is a private school and what district he lives in is irrelevant).
Yes, there are some rumors that he was about to lose his starting job (cannot confirm or deny those rumors), but there are several teams in the Tampa Bay area that could use a good QB. It seems a little odd that the family would just pick up and move across the state, taking the kid with them, in the middle of the season, even if the kid had been told he was being benched. Seriously, think of the costs associated with that decision -- selling a house, buying a new house, moving across the state, forfeiting any tuition they paid for Jesuit, etc.
For what it's worth, if I were ever in that position, I'd want to know that I'd be transferring into a good situation where I had assurances that I'd be able to play right away. That means I'd need to know the new school's situation, the new school's coach and be reasonably confident that I'd be able to play this season at the new school. I don't think that last item is something that you can get cleared/approved in advance by the FHSAA or whoever else has a say in that determination.