Yes, employers during WW2 started offering health care as a fringe benefit because the US had wage caps. Even earlier, the government required licensing of doctors, the original purpose of which was to drive out Jewish and Black doctors.

https://www.amazon.com/Competition-Monopoly-Medical-Care-Fre...

But the big government push into health care happened in the 60's.

Another big driver of American health care costs is the FDA:

https://www.amazon.com/Regulation-Pharmaceutical-Innovation-...