However, some of these private toll roads did go under. And then a government (fed or state) would need to take over to ensure a continued route between the places served by the toll road.
And in those cases, the government often also continued to run them as turnpikes - or as we would say now, toll roads. Sometimes the government bought out the original owners, too.
Then too, there were turnpikes that made it through to the 1930s in private ownership.
Anyway - looked at historically, “free” highways are a very recent development in the US. More of our history had the majority of the highways being paid/toll than not.