When comparing American and European racing, all you have to do is look at their roots.
The first scheduled, organized motoring event was the Paris-Rouen rally in 1894. It ran several hundred miles over country roads. Later races were also over open roads or in cities until they started building racetracks, which were made to look like roads, hence "road courses".
When Americans first started racing (about the same time, of course, but without the organizers and prizes), they took their cars down to...the local horse track!
There you have it!