What you're describing is the lack of a normal market, and even that only applies if you have insurance. For the millions of people without insurance, they do indeed shop around. It is very much a capitalist system, since the ownership (& control) of the system is not in the hands of the workers - in insurance companies, hospitals, pharma, etc - but in the hands of wealthy shareholders.

To be fair, I suspect your definition of capitalism is very different from mine...