The solution is very simple - if a player is hurt and play is stopped, that player can't return for the remainder of that possession. It can be sold as a "player safety" measure, and will certainly make teams think twice before losing a key player in a big spot.
To remedy the idea of losing a QB who took a hard hit and needed a play to recover, maybe make it cost a time out for a player to return in the same possession. I'm not crazy about stuff like "injury timeouts" the same way as I hate the "coach's replay" garbage in the NFL - stuff like bad calls or injuries shouldn't be something else a coach needs to deal with as a 'strategy', as they have enough on their plate just coaching the game.