Why wouldn't a player just say, "I will go to your school to play football, but I am not signing a LOI". It sounds like the LOI is a contract solely on what the player has in agreement to the school, but the school owes nothing to the player in the LOI. The Financial Aid Agreement is what is what is providing the actual scholarship to the player. By signing the LOI, the player is forced to uphold his agreement to play for the team, or face restrictions if transferring. By not signing the LOI, if the player decides to transfer, it sounds like he would be able to transfer without playing restrictions.
Signing Day Options
Signing Day Options