Depends on how much you think injuries are directly related to how an athlete plays the game compared to how much you think injuries are random.

If an athlete plays like hell in a handbasket and does well because of that, then injuries resulting from the playstyle are connected to in-game performance, and healing faster from them would probably be an unfair advantage. Making such a drug fair game might have the consequence of encouraging athletes to be more reckless, because they can gain rewards in the game and suffer fewer injury-related consequences for doing it.

But if an injury is random, a matter of pure bad luck, then couldn't you say that it would be in the interest of the sport itself to have the player healed up and playing again as quickly as possible? If there was no effect on in-game performance, it would only be ensuring that teams had their full complement of players available as often as possible, and that the sport itself maintained a high level of competition, unhampered by long injuries to some of its best athletes. Maybe Bobby Orr would have played another five years instead of being forced to retire from hocky at a young age. Maybe Johann Santana (or countless others) would still be pitching at an elite level instead of being hampered by the effects of long term injuries that were largely outside of his control.

I don't think it's a real clear cut question.