Here at BB that might work. Basing the DQ soley on injury status has all kinds of potential for a scam in real life. Let's say a bench player is fouled by a key starter; wouldn't it be tempting to fake a severe injury and take the bench player out of the game, just to get the key player removed. If that were to happen, key players would stop playing hard on defense. It's best left to the official's discretion.
NBA players are DQ'd for Flagrant 2 fouls, whether or not the fouled player has to leave the game. I have not seen that here, but it might not be a bad addition, only if the other fouled player has to leave the game.