France, Spain, Germany, Argentina, Brazil, Mexico, South Africa are hardly "small" and while few nations are as large as the US, these are certainly examples of how dozens if not hundreds of transmitters and boosters can be used to cover a very large area.
In the continental US, it might be appropriate to do one network for each time zone, or, at least, East, Central and West.
In fact, our RDS FM data system was originally devised to allow automatic search and frequency change to find the strongest signal of a network so a person driving across an area of a nation would never lose the signal.
Brazil and Argentina have plenty of commercial stations, South Africa (where the state networks have low ratings) has them also. Mexico is all commercial as far as I know (although they have La Hora Nacional, which is a program, not a national radio network per se).
When you said 'national networks' what came to mind was countries like Norway, Finland, Sweden, Iceland, Denmark, Switzerland, Austria, and the like, where national networks not only have nationwide coverage, but very high ratings compared to their commercial radio sectors. And if you look at the populations of those countries, where national networks appear most successful, they range between 5-10 million (300K in the case of Iceland). Germany is about 90 million people, but the national radio network is divided into individual state radio networks.
As for the idea of having national networks in the US, it may or may not work. The PNW has little in common with California, just as California and Texas are different from each other, and NYC and Alabama are different from each other. Even in Canada, where there is a large national network (the CBC -- two of them, if you count the French and English ones as separate networks), the only 'national' programming of note is the news broadcasts and a few time shifted national programs, but a lot of the dayparts are local to the provinces and individual metro CBC outlets. And although the CBC gets high ratings, commercial stations gain higher ratings in many Canadian metros.
I'm not trying to say 'live and local' is the answer, or imply that there is no place for national radio. I enjoy CBS's national news programs, and many talk and news shows are national in scope. But I think there will always be segmentation in radio as long as there is OTA radio in the US.