Interestingly, we have one here opening this summer. A very large private landowner is building a cut-through between two feeder roads that connect part of Tallahassee to a rural community just outside the city that otherwise requires a lengthy detour to get to. (Tallahassee is a wheel-and-spoke city).
The builder is making it a toll road until the road is paid for and then ceding it and the land it runs on to the state.
Another variation: the financing to build that specific road may have been structured so that all or part of its repayment would come from proceeds of its tolls, and not from the taxes that cover all roads in general. There are also cases where the privatization works in reverse: the contract involves a constructor/operator that builds the road and collects tolls from it to pay off the loans and make their profit, and once that is fulfilled, the road becomes public at the end of the term.
Actually, I think a “fair use tax” is when you’re designing your own toll road, and you incorporate elements of some other civil engineer’s design, but not so much that it constitutes plagiarism, so you don’t have to pay a full royalty, just a nominal fee.