Of course it would work for the US, if the US had sufficiently powerful insurance agencies. If hospitals and doctors want a certain amount of money and insurance agencies have the power to say no, these healthcare providers just won't see any patients or only rich ones.
This is how it works in Germany for example. As a hospital you have to accept the money you'll get or you won't get any at all.
The healthcare market in the US is not balanced and this gives healthcare providers to increase prices to ridiculous levels, especially in rural areas.