What may happen, or change, after a game is over in not within the game official's responsibility, or control. However, the game officials judgment, as to what level of remedy is appropriate for behavior during a specific game is EXCLUSIVELY decided by the game officials, and pertains to ONLY the specific behavior being assessed, and it's potential effect, on that particular contest.
Coaches (and/or players) are not REQUIRED to agree with those decisions, but they are REQUIRED to accept them, and whatever consequences may be assigned. There is no authorization in either NFHS 1-1-6, or 1-1-9 for any mandatory consultation, discussion or appeal, although game officials can CHOOSE if, when and to what, if any, extent, they alone deem necessary, to consider, what may be perceived as relevant additional detail.
Ageless advice still prevails, "if you can't do the time, DON'T do the crime).