A childhood belief about getting older

As a kid, I noticed that kids were flexible and adults were stiff in their movements; adults also seemed to be really interested in exercise. So I assumed that as you got older, you had to be careful to exercise & keep moving so you didn't stiffen up and die.
With this state of affairs in effect, it always bothered me how if people broke their bones, the doctors immobilized the broken part so it could heal. So I wondered why doctors thought this was a good idea, given that the part of their bodies that got broken got older faster from being intentionally stiffened by a cast.
I figured that having a part of your body that had gotten broken getting older faster was better than having it fall off entirely, because broken things were thrown away in the garbage. I thought once a limb had been broken, it would rot in a race with getting gangrene if you did not get a cast on it. (This also explained the bad smell inside of a cast as a race between aging and rotting.) This also explained to me how people who had been in an accident were somewhat broken for the rest of their lives.
All of these ideas made me very careful to not break a bone when I was a child, and to be very sympathetic & compassionate to people who had broken a bone.