Country size has nothing to do with it; it's all in the lobbies.

Much of what's wrong with American healthcare could be fixed with a few pieces of federal legislation:

1. Any medical practitioner who deals with one health insurance provider has to deal with all of them. Likewise, all insurances have to accept bills from all licensed medical practitioners.
2. There are limits to how much can be billed for a certain procedure within the health insurance system.
3. There are limits to how much a health insurance is allowed to charge for the basic plan relative to income.
4. A health insurance's basic plan must cover at least a certain set of medical procedures (but is allowed to cover more). These include all regular life-saving procedures and a range of preventative ones (e.g. semiannual dental checkups).
5. Health insurances are not allowed to deny basic coverage due to pre-existing conditions.
6. Deductibles are banned.
7. Copays are regulated.

This gets rid of the "out of network" bullshit and basically turns the American healthcare system into an approximation of the German one. The German system is one of the most expensive in the world and generally considered to be of middling quality compared to other wealthy nations but it's half as expensive per capita as the American one; based on free enterprise (with a fuckton of regulations, which is normal for the medical sector); and wildly more effective than the American system, which doesn't even rank among other developed nations.

The only reason the USA don't have a better healthcare system is that lobbyists spend an unholy amount of money to ensure it doesn't and lawmakers are willing to do whatever the highest bidder tells them to. Size and diversity have nothing to do with it.