You're halfway there on this one, but I think you're too much of a free market guy to see the other half of the problem.
Free markets only work out well when both buyer and seller are free to walk away from a bad deal. This is in large part why prices for cosmetic surgery have bucked the trend. If boob jobs cost too much, people won't get them, and that exerts downward pressure on prices.
For the life-saving/life-prolonging aspect of medicine, that isn't true. Diabetics will willingly pay their entire income and even go into crushing debt to buy insulin at any cost.
Yes, this is a situation where we need an intervention. Essential healthcare should be treated as a public utility. If a city wanted to jack up the price of drinking water by 300% its citizens would never go for it, and the city has a mandate to provide water at an affordable rate so that never happens.
The biggest problem with government intervention/Medicare for All/etc. is, of course, that the government is in the pockets of the medical and pharmaceutical companies who would be happy to negotiate a pork-barrel bonanza for themselves behind closed doors using public funds. So that is not the answer either, however much the left might want it.
The free market is not the answer here. The best I can come up with is establishing local clinics and hospitals that are organized as public utilities rather than for-profit entities, and eventually generating the political will to crack down on exploitative for-profit healthcare.