I was told by someone that has been a AD at the D-II level (a lot of FBS friends) that you don't do mid season firings not only because how it affects the kids but if you have a shot for a bowl game still, you want that extra time for player development.
You can fire the head coach at the end of the regular season and have someone on staff be there interim head coach.
If the players do not want to try during bowl prep due to their head coach being gone, it won't go unnoticed by athletic department staffers or others that may return on the next staff.
At some schools like Florida or Tennessee, I don't think mid season firings is as much of a deal like some place like Nebraska where that player development is more needed.