A big part of this is that the playoff setup makes it unlikely for any specific team to win the NC, even the 1-seed.
If this was back in the day and OM was simply facing a bowl game for a potential NC, OM would keep him to try to win it. The reward would be worth the risk, easily.
But a 4-game gauntlet where no team is anywhere likely to survive, no, it's not prudent to allow your outgoing HC to stick around and mettle with players and personnel.