Cars have nearly nothing to do with this. It started with the industrialization of farming.
Farm towns existed at normal intervals because it took a much larger labor pool to manage them. 200 acres was a lot to manage about 100 years ago. By the 1970's 400 acres was a normal sized family farm in the US.
Modern machinery can cover nearly 200 acres in a day. There is no reason to have thousands of people per small town anymore. It takes a tiny fraction of that manpower to achieve the same output.