Suppose, instead of purchasing road services from the government, (now via gas tax, later via mileage based user fees), travelers would purchase transportation services (the right to travel at a location at a time for a price) from independent road service providers. Road service providers (RSP) would purchase capacity from the infrastructure owner (presumably the government). If an RSP’s customers over-consumed the road, the RSP would pay a penalty. RSP would charge its customers accordingly to maximize profits in this new competitive market.
What does this allow?

1. It allows competing RSPs to offer a variety of bundled services to customers (a per use charge, a charge for a the right to travel 10 times per month, or unlimited service, or service bundled with cell phones, or insurance or other services e.g), but to each have different bundles. RSPs are likely to be better at product differentiation and price discrimination than governments with omnipresent political and equity concerns.
2. It allows the government to stay out of the data ownership business, it would be responsible only for identifying which RSP a traveler subscribed to, and thus would eliminate “the government is tracking me” problem with road pricing. (We still have big brother business is tracking me, but if you have a cell-phone or credit card, that game is already lost)
3. It provides new markets for private industry. This could be an app as part of a cell-phone or GPS or in-vehicle service (e.g. OnStar) or insurance (AAA, Progressive). The only technology standard that would need to be established by the government is a simple (e.g. RFID) sticker adjacent to the license plate verifying the RSP and the government with inexpensive RFID readers to count the number of cars on each link by time of day with the RSP. The private firms would be responsible for monitoring their own customers.
4. It provides a more stable revenue stream from government, which is getting revenue directly from RSPs who bid on road space. In congested areas, road space would go for a higher price, in uncongested areas, RSPs would negotiate a per-use charge with governments.

One can poke some holes (faking RSP, like faking insurance or fake license plates or fake drivers licenses), but I think the idea is worth exploring.