The argument about the US being too large for X gets made for all kinds of X, all the time. It tends to not make a lot of sense. As the size of the country goes up, so do the available resources. Maybe there will be a couple of layers of additional organizational overhead, but there's going to also be access to a lot more economies of scale so it should be just a wash.
Why would health care be harder to scale up in terms of the size of a country than, e.g. the military or the fire brigades?
As for diversity... I don't buy it for your specific example. Switzerland has:
- Four official languages.
- A federal system with similar levels of decision-making devolved to the cantons as to the US states
- 11 political parties significant enough win seats in the parliament
- High levels of immigration: 30% of the population are immigrants.
The reason Switzerland shouldn't be brought up is that the health care system isn't particularly good, just different. In particular it's the second most expensive in the world.