But I wonder what the market would be if everyone actually had to choose their own insurance and didn't expect/demand (especially the public sector employees which really skews the market price) insurance with their job
It would be like any other commodity. You'd have a high end end a low end. Since healthcare is largely a "for profit" deal, the luxury care would be very good and the low end would be very bad or minimal. No different than cars or clothing or housing.
From what I've heard with HMOs (including some employer-provided or subsidized ones) we already have that spectrum you describe.
In fact, uh, we already have that with education. Not sure what your point is.
The average (or at least median) price point would still be lower and we would have more freedom to spend what we CHOSE to on these items.