Interestingly this wasn’t the case in living memory in the USA. The insurance cartels have effectively greatly increased prices while commensurately lowering the standard of care.
Medical institutions have been kept onboard with massive increases in revenue that subsequently led to expansions of the institutions that are now dependent on that higher revenue to exist.
My dad told me in the 90s to avoid injury because the family could not afford healthcare. I distinctly recall hospital bills being in the tens of thousands even back then.
I doubt newer cancer care, medicines, imaging, or other care would be cheap in any world, with or without insurance.