Securing the corridor is not just a military problem.
Alex Tabarrok writes blithely in Toll Collect:
I see toll roads, most privately operated and some privately owned, as the road of the future. Road pricing can not only reduce congestion it can also help with accident externalities.
The libertarians at Samizdata and Transport Blog are also dreamily infatuated with this model; but the one flaw I see -- and no one seems to be able to answer it except by waving their hands wildly and talking about "mutual advantage" -- is how do you secure the corridor without government's power of eminent domain? Talk all you like about negotiating with private property owners; the transaction costs involved cannot be surmounted; you need the government's heavy hand of condemnation to secure a road in and between metro areas -- which is of course exactly where you'd want to put the new roads, if you could garner the political support to put very many new roads anywhere.
I might like to believe otherwise but I am a realist.
And if you are merely talking about private financing of roads already designed and with a route secured by the government, then I don't think that's much of a big deal.
(Note: This post doesn't reach the issue of pricing road use, which I think is another one of those attractive ideas with superficial appeal and which also faces insurmountable practical, legal and political problems.)
UPDATE: The very interesting commments buttress my point. In order to avoid condemnation, eminent domain, you have to come up with a Rube Goldberg set of assumptions about how to create a rather vast transport corridor through the negotiation (along with feints and counterfeints) of rights and options. The suggestions, while having some theoetical appeal, seem to me to ignore the difficulties of negotiating with thousands of owners as well as the practical limitations on where new corridors could/should go.
I suggest that anyone familiar with the very reality-based world of real estate will see what I mean.