Also, exorbinant salaries and good hours are not to be found in the hospital system. Yes, specialist doctors get paid "well", but not exorbinantly, when adjusted for required training, education, experience, and opportunity cost. In private practice, the hours are better, yes -- but only in certain subspecialties. But this is like saying major airline commercial pilots should just fly private charters for a better lifestyle, or that software engineers should just work at hedge funds as quants for better compensation.
It's the hospital system, not private practice, that shows us a healthcare system where doctors are being put to their unique purpose of advanced clinical treatment. And that's where the market is failing.
Healthcare requires the hospital system to provide the most advanced and emergent forms of care, and that is where doctors are overworked and undervalued.
As for the free market, I wish you were right that it could fix the US healthcare system. But patient health is, unfortunately, not valued correctly by the market. The market rewards chronic treatment, whereas society prefers one-time cures. The market tries to monetize patient-doctor interactions, whereas society would prefer fewer doctor visits with fewer hospitalizations. The market treats doctors as a cost center whose hours needs to be billed out at a profit, and society would prefer doctors as a value center who are given the professional leeway to use clinical judgment in assigning time to cases and patients.
I love market systems, but only when they work.