I don't recall who first relayed this to me but I believe the answer to the question in the title is "path dependence". Modern (US) health insurance started off as hospitalization insurance and was originated by hospitals themselves. It covered hospital procedures such as surgery etc.

We should note that dentists and opthomalogists do not typically operate from a hospital setting, at least not in the early (1920-1950) era.

Over time it was spun out of hospitals and extended to more medical procedures. The tax advantage of having employers pay for coverage began to dominate the market and has led to the current state of the medical marketplace. But the original dichotomy remains. "Health" insurance covers things that doctors do, and mostly those things that happen in hospital settings.

There is an interesting article [1] that has some of the history of group health coverage which I found just now.

[1] https://www.peoplekeep.com/blog/the-complete-history-of-empl...