I wouldn't worry about your best players getting injured because you don't have a good doctor, I'd worry about it because you keep starting them in pointless scrimmages so you're playing them in an extra (useless) game where they could get injured and killing their gameshape in the process which likely makes them more susceptible to injury overall.
I'm also not sure why you're carrying 12 players if you only like playing 7-9 of them. You're just paying extra salaries every week which cut into your profits.