Workers comp stepped in on a few of them although it was debateable as to how those injuries even happened. The only one I can think of that could be directly attributed to mechanic work was the shoulder surgery. That injury happened with reinstalling a gas tank into a Subaru. The tank was empty/light but I just turned wrong, caught a white flash, and the arm dropped dead on me.
The others were covered to some extent by private insurance and I paid the balances due over time; as painful as that was financially.
A lawyer on the shoulder injury tried to get me at times to lay the rest of those problems on my employers by insinuating that if I were willing to claim even the tiniest bit of a problem related to my current job he could cash in for me. I refused to do it; that’s just not me.
I know what you mean about pushing cars. Every day it’s round up the other guys and shove them into the shop. Even worse, it sometimes involves pushing them back out when a customer doesn’t want a repair or wants to think about it for 2 weeks.