re: Does the offense get better going forward if T. Hill is out?

I think the way you correct this is go where it hurts. Fines for players should be a percentage of game checks. I don't know if that number starts at 5%/10%... or what, but these few thousand here and there don't mean much when the guys are getting a $100k per check.

Since the players are protected by the union, you will be limited on how much you can go after them and you cannot take more than a check if they are playing (need to earn at least a minimum amount)

However, you can then go after the teams. If a player is injured in a game and has to leave the game (and miss multiple games); then the league should look into whether or not it was a dirty/unnecessary play. If it is, then the offending team should be responsible for the injured players game checks until they can return (salary cap rules apply). You will start seeing teams/coaches being held responsible for these types of hits.

It is drastic, but unless you take drastic measures there are no real incentives to coach it out of the players.