False premise. One can establish such roads by law (e.g. desired routes) but have the private sector build and maintain them afterwards. Same with post offices, where charters are issued to private owner/operators.
The private sector owned and operated (and still does) huge interstate railroad networks; the same can be applied to interstate highways. No need to gouge people for taxes to fill a “trust fund” whose end is questionable, never mind being a Ponzi scheme in and of itself. There are no flaws with the concept of privately-owned roadways whatsoever, other than the government regarding it as a flaw when they want control of it. No toll roads given over to private operators have become “financial disasters” either—the financial disaster was having them “free” to begin with, and the trust fund is exemplary of the real disaster.
Your point about the railroads is valid in some ways, but there is a major problem with it: How many of these railroads were constructed using enormous government resources as well as the government's power of eminent domain to forcibly seize private property from its rightful owners?
In terms of privately-owned toll roads and their financial stability ... Did you ever wonder why most of the investors that purchased the long-term leases on these toll roads were foreign companies? It's because institutional investors here in the U.S. were too smart to get involved in them. Having the governor of Indiana running around highlighting his credentials as a smart leader by pointing out how badly he screwed the new "owner" of the Indiana Turnpike makes that point clear.