The free market works great for things like Lasik surgery and cosmetic surgery. Patients shop around, get referrals, make a call and pay.
The problem in the US is that's not free market. How can it be a free market if the price isn't posted or isn't known until after the purchase? How can it be a free market if people with good insurance don't care about the cost because they only pay some insignificant portion of it?
Discount laser eye surgery has its own issues with deceptive advertising, misleading pricing, patients being rushed & not fully informed of potential side effects or receiving poor post-op care. People really need to research thoroughly before using a coupon for their laser eye surgery. No one should expect the market to just provide a quality product. That's foolish thinking.
And many of those issues of rushing patients and not explaining risks happens in public systems too. You think doctors work for free in those systems?
And in terms of quality you’d be a fool to not check even in a public system. I worked in the healthcare field and quality of doctors varies widely.
My point was the free market you lauded for Lasik is a mixed bag with some potentially good value for money, but also deceptive salesmen muddying the waters for consumers to make valid comparisons on price & quality. It's no panacea.