At some point this is true. But there is Great value in learning/being able to push through adversities. Yes, that includeds injury.
At the '88 Trials, I had to get through three matches with one fully broken rib, one cracked, and a heck of a lot of soft tissue injury. Taped up the ribcage and sucked it up.
Looking back, I don't think I could have done much better than I did, ending my run 1-1/2 matches away from the Olympics. I feel very good about my performance. In hindsight, this worked to my advantage since my competitors did not expect me to fight the way I did.
Yes, the recovery sucked, but I don't think I exacerbated the injuries in the last three matches. It did change my fighting style, however.