They wanted to introduce the VMT in the Netherlands, but it failed due to opposition. The greatest alleged effect would have been a reduction of congestion by pricing people off the road and reduce peak hour travel. However more recent studies found out mobility is less price-elastic than what was previously assumed, as even $ 9.00 gasoline didn't have any effect on the mileage driven.
Though the cases of the United States and the Netherlands / Europe are different. In Europe, mobility is just seen as a cash cow, European motorists frequently generate 4 or 5 times more revenue than what is actually spent on road infrastructure. It's not necessarily a funding issue, though European funding for roads remains tight, but that's due to politics, not because motorists aren't paying enough to maintain and expand the road networks. There's enough money generated by motorists to 10-lane every rural freeway and keep them toll free.
What strikes me most is that the U.S. gas tax hasn't been inflation adjusted for two decades, just like some toll roads haven't increased their tolls for years while the cost of upkeep and expansion continues to increase, often even faster than the rate of inflation. Which means resources to fund roads are dwindling.
A gas tax is not the only way to generate revenue. In Europe people often have to pay an annual road tax, which in some countries may exceed $ 1000 per year. Furthermore, high taxes are levied on motor vehicles in some countries (for instance 75% tax in Denmark, and a 25% sales tax comes on top of that, effectively resulting in a 100% tax on cars). So there are basically three types of taxation on motoring; ownership, usage and fuels, each of which is in fact sufficient to fund the road network operations.
I don't think it's a good idea to follow the European example of over-taxing motorists, but some "thinking outside the box" may be required. It's a taxed road, it's a toll road, or it's no road, someone once said. There is no such thing as a free road.