This option doesn't work because healthcare can't be a free market. Car insurance companies have to compete not only with each other but with alternatives like not owning a car at all. There is no alternative to being alive, so health insurance companies can effortlessly collude to raise prices across the industry knowing that they have the most captive customer base possible.
(b) if we had a reasonable market then some people could have an alternative like paying out of pocket
US healthcare has to compete against cheap healthcare in mexico or whatever
A good first step would be banning price discrimination for medical procedures. Right now you get three different prices for "I pay", "insurance pays", and "insurance denies and I pay". People can't tell you what those prices will be. The whole point of insurance is supposed to be to derisk these kinds of decisions, not increase uncertainty and risk. Attempting to use insurance and getting denied can 10x your cost, so what is the purpose of the insurance?