In the early days of the U.S., privately funded roads run for profit definitely existed. There are government-run toll highways that make money in excess of their maintenance costs, which suggests it should still be possible, if the government didn't already have the prime routes.

At any rate, the interstate highway system was a project to make the transportation network more robust for the purposes of national defense, inspired by the German autobahn. Centrally planned solutions to make the U.S. more like Europe won't always have the expected consequences.