Yet here we are. Remember when Obama fought to have healthcare prices made transparent so that we could shop for the cheapest medical treatment, and that was beaten back severely by the lobby? The compromises the ACA made to bend over backward for for-profit insurance companies were an example of how much power the lobby has. I think if we've learned anything is that we need to go all in on single payer and completely remove for-profit insurance, IMHO, because of exactly what you're saying about the free market: it doesn't work for certain things (if anything, really): military, education, healthcare all the three classic failures of the freemarket. I think this is why all the dems are embracing Healthcare for All: everyone is getting screwed by healthcare except the 1%.
I think the free market does a good job of solving problems, just not of deciding which ones are worth solving. The military follows a hybrid model that (mostly) works, where a semi-free market is created and guided exclusively through governmental leverage, theoretically giving the best of both worlds. Utility companies work a similar way, as do (I think) some first-world government-run healthcare systems. I think the ACA was aiming for this type of thing, but was so hamstrung by compromises and by the sheer complexity of the system it was trying to reshape, that it ended up being a pretty mixed bag.
Maybe in the case of American healthcare, the current state of things is just such a horrible rat's nest of problems that we really do need to burn it all down and start over.
The insurance companies and the AMA were vehemently against Medicare when it was initially proposed. They fight for it now. Given all of the established interests in the medical system, and the amount of money flowing around, any reform that is actually going to make a major difference is going to be one that they strenuously oppose.
