It used to be like that - here’s some evidence.
http://www.oftwominds.com/blogjuly09/healthcare07-09.html
I have been afraid to delve into HR 3200, but I did peruse the 1990's "HillaryCare" version, and there was a clause in there expressly forbidding paying your doctor yourself for your services.
Thanks again for the link—Absolutely loved the 1950’s OB rates!!!(Of course, it must be recalled that even auto wages back then were around $35/week. I’m sure there’s a way to check this, but I want to be a writer, so...facts do not concern me)
1961, first baby. My wife was in the hospital 3 days (normal stay)..$180.