You've also probably lived your whole life in urban areas shaped by personal injury lawyers and don't spend your life doing hard labor so you may not have gotten any serious cuts or broken bones because if your lifestyle.
I’ve got scars all over my body from cuts and scrapes. Some even needed stitches, back when that was a thing (now we just use some magic glue)! I’ve been lucky to never have a broken bone, but it wasn’t for lack of trying!
I didn’t live in an urban area until I was in my late 20s.
It didn't always have to turn into an infection as there are plenty folk methods of preventing that from happening used throughout history - from wound cauterisation to my regional bread + spiderwebs.
The latter was given a scientific explanation in modern times: the webbing contains live penicillium fungi in quantities sufficient to act against microbes.
It's very rare for a minor injury to become seriously infected to the extent that the patient's immune system can't fight it off. Even before the discovery of antibiotics, amputation was typically only used as a salvage therapy in cases of gangrene. They didn't reach for the bone saw just because you had a serious infection.
This is why most women spent most of their adult life pregnant and there's still lingering moral pressure to have children. Societies, especially as they advanced, had real trouble maintaining population through reproduction alone.
