People like you think the government should solve a problem that they themselves created.
In theory, but in practice there are many markets where that simply doesn't work, mostly due to natural monopolies, such as any type of infrastructure, healthcare or education, where competition is impractical or impossible, equal access for everyone is extremely important, and costs are high.
Still, nothing really stops competing methods and prices for teaching to competing levels.
By what fraction will the new set of tweaks have to shrink costs to pay for the last 30 years of the private health care market's failure to deliver on its "more efficient" promise? Remember, it has to cut them by 50% just to break even, and it'll have to go further to make this experiment worthwhile. A lot further.
Spoiler alert: it won't even get to 50%. It won't even get close to 50%.
I might be wrong. Maybe price transparency will lead to a 50% reduction in prices in the next few years. I doubt it, though.
A few years back I broke my wrist while bicycling across England. I was patched up and casted a few hours later, I think the bill was about $200, as a foreign tourist. It wasn't even enough to cover my travel insurance deductible. This would have cost me about $5k in the USA.
I agree that the free market works fine, for those who run the market.
All you have to do is ask a doctor "Please don't put any of this in a file until I have insurance next week". It doesn't mean anything to him to add the dates later. It's in his best interest, otherwise he won't get the cheddar.