What level doctor do you carry? I know quite a few managers who carry higher level doctors and almost never deal with injuries. Could just be luck I suppose, but I think if managers are complaining about injury length and they don’t even make an effort to carry a doctor better than the worst possible, I don’t feel bad.
Doctors cannot (and should not) prevent/remove all injuries. It wouldn’t make sense. I think you are undervaluing the importance of doctors saying “Investing in doctors to counter injuries is similar to take a US$100 paracetamol/tylenol when you are suffering from a kidney stone.” But you are welcome to disagree.