I understand that this is how it works, and is a completely legitimate argument, in the ideal model with essentially limitless choices for the user. I do not believe it is a legitimate argument for private roads, however, because there are not limitless choices as to what you take to get to your destination; often there few*. "Maximizing efficiency" in all cases means finding the most profitable balance between cutting corners on your road and getting people to drive on them, and a decrease in the number of choices means that balance starts tipping heavily in favor of corner cutting because the number of people driving on your road starts becoming more and more inelastic. The barrier of entry to making new roads being quite high means that drivers are pretty much stuck with the corner cutting whether they like it or not.
Private ventures may have a vested interest in making the roads good (which pushes the balance away from corner cutting) but if you're the only game in town, you're going to cut as many corners as you can live with.
* While you can take roundabout ways, you are virtually always going to end up taking the same stretch in several of your routes.
The roads themselves are not "owned" in the "model" - the private enterprises just maintain them. Because you can drive on the roads either way - the privatization is just in who maintans them and gets paid to do so.










