Interesting. I in fact did drive a tow truck for a few months, same time period (1982). No, I didn't make the cut.
Didn't make much money, either. I learned a few things, and then took it with me.
That said...big difference, pre-1982 cars and today's cars. I never saw a wreck with a wheel broken off. Oh, it happened, but not frequently...car would have had to really been destroyed for a wheel to come off. Now it seems, someone starts sliding and hits a curbstone at speed, and the first thing to go, is the wheel...and brake and spindle and part of the front suspension. Or half the fragile lightweight New-Age rear axle. This, even on these massive Bro-Dozers of recent years.
Bumpers were chrome (or painted metal on trucks, which were utilitarian vehicles back then). They mostly stayed put. Only the Trans Am and a few other sporty cars had rubber colored bumpers. I never had a wrecked TA in my short time.
But the bumpers stayed on. So did the doors. And if one came off, lifting it would have been a two-man job. I had to take the door off my Pinto, and yes, two big guys, both wondering about hernias.
Today's cars just EXPLODE with bumpers, doors, all kinds of fluids, on even walking-speed crashes.