The telecommunications industry has avoided the extremes of congestion and under-use by adopting pricing rules and investment criteria that make the best use of scarce resources. They raise prices at peaks periods and then use those revenues to expand peak-period capacities. Competition ensures that the industry develops in ways that are responsive to customers. There is no reason to think that private roads would not be managed in similar ways. Furthermore ownership is an important element to proper stewardship.
Owners stand to gain from the proper maintenance, use, and development of their assets.
If people owned elephants they would be taken care of and would not be endangered. Now of course, elephants are not owned because they do not have as much value but the reason why they are not owned does not detract from the point that if they were owned they would not be endangered. Ownership also promotes innovation. Telephone companies have developed phone cards systems for their public phones. Toll-roads have also developed ways of collecting tolls without even needing cars to stop.