> If people can't pay as much, the only thing for them to do is drop prices.
Or not offer the product at all. One problem with this entire area is that "healthcare" is really not one service/product area, and it is probably a mistake to treat it as such.
To be transparent, I don't share your optimism about market solutions to problems like this in general (more about their implementation in practice than theoretical benefits) but I can see how it might help with parts of the routine healthcare. However, when you are talking emergency and major treatments, it's well into the range where direct consumer driven decisions are more likely going to mess up the incentives badly.
If you are lucky enough to have the time (often not true), most people can become reasonably expert in their own disease state and treatment options. But that is a tiny slice of what is going on in a hospital system for example, and it's completely unreasonable to expect people to become informed enough to make good decisions there. If we want to benefit from market forces here, it's probably much more effective to have large (or single) payers who understand what the standard of care should be, and can encourage price competition from providers.
It's worth noting that in theory this is what the insurance industry does in the US, though, but is an expensive mess. Another confounding factor is that many obvious price discovery mechanisms will be completely unacceptable to most people.
Honestly, it's a mostly faith-based argument that a cash-based market approach can find a better global solution than universal health care, at least in a relevant amount of time. It's really hard for me to see why the country should take that risk when there are well understood and well modelled approaches (albeit imperfect) that should be able to reduce costs by at least 1/2, probably more.
Why not start there?