I don't see the natural monopoly case, although there is definitely scope for rent seeking. Roads, rail, air, and sea are all in competition with each other, although one may have the technical advantage on a particular route. The nature of network effects also puts pressure on owners of particular networks to connect with other transportation networks, rather than to operate in silos.

An interesting historical note on private rail development, is that in 19th century America, only the Great Northern Railroad rejected government subsidies and it was also the only profitable railroad in that era.

As for how I think privatization should proceed, I tend to be a gradualist. So, I would start with the easy stuff, like allowing home-owners associations and other neighborhood organizations to take ownership of their roads, as well as allowing private development of parallel routes where there's tons of traffic. At the same time, I would introduce mechanisms, like tolls, that introduce pay for use of state owned roads. That's where the incentive to reduce state inefficiency really starts playing a role. Retailers may want to buy some of the roads, since they may be willing to take over the costs in order to facilitate customer traffic.

Congestion on public roads that do not charge tolls is another example of a government-created tragedy of the commons. If roads were privately owned, owners would charge tolls and people would take the toll into account in deciding whether to use them. Owners of private roads would probably also engage in what is called peak-load pricing, charging higher prices during times of peak demand and lower prices at other times. But because governments own roads that they finance with tax dollars, they normally do not charge tolls. The government makes roads into a commons. The result is congestion.