I agree with you totally that being physically active is important for being healthy.

And I think there's something to be said for your point that experiencing pain and seeing yourself recover from it can be helpful for processing pain psychologically. You could look at it as sort of exposure therapy for pain.

But I also think that the kinds of pains you get from exercise are quite different from the psychological experience of pain from a serious injury and the former doesn't really prepare you for the latter.

It's hard to explain unless you've been there. Most of the time, pain is a signal from your past telling you about something you did. It's your body's way of saying "don't do that again". But when a severe injury happens, it can also be an omen for your future. Your body saying "no, you don't get to do that anymore".

Processing that is difficult, especially given how uncertain the signal actually is.