Why does the U.S. have so many general-aviation aircraft?
Part of the reason is also historical. After World War II was over there was a large number of veterans with flying experience returning to a country that suddenly had a massive surplus of small trainer aircraft.

While the US expended huge amounts of resources on World War II, it was largely untouched by the destruction that many other countries suffered. This meant that instead of having to rebuild, the US could focus on growing the economy. Though GA declined in the Great Depression and was suspended during World War II, there had been a similar situation after World War I that had gotten the industry started.

Small aircraft were much simpler then, with a much lower cost to build and certify. This made general aviation relatively much cheaper. Also, while the US certainly had a highway system, the interstate highway system had yet to be built. Commercial aviation service was not nearly at the scale it is today and was still fairly expensive. This made general aviation a much more reasonable option for traveling around a large country.