That's a classic "Tragedy of the Commons" scenario. The electric car benefits are great when only a few are on the road, but when everyone gets one it turns into a problem.
That will become a problem in the US as well, since US highway construction and maintenance is mostly funded from motor fuel taxes.
Highway maintenance is already a problem in the US, but not because of electric vehicles, it's from increasing efficiency of fossil fuel vehicles and the political refusal to raise fuel taxes to balance the maintenance costs with the tax revenue from fuel. If electric vehicles do become a significant proportion of vehicles on the road, the pragmatic thing to do would be to charge for mileage based on the odometer and vehicle weight.
How is the odometer data supposed to be collected? Weight is easy, though. I guess you could let the car phone home a couple of times per year, but the consumer still owns the car and can do a lot of shady stuff with the odometer, I imagine. Better to just use a flat annual fee with modifiers for weight. Trucks and other business vehicles can be assumed to travel a lot, so higher taxes for them.
I think the car-to-car variation in annual mileage traveled is too wide to fairly assess an annual fee. A secured odometer box checked during periodic vehicle inspections would be enough to reasonably raise the bar on mileage, but unfortunately more invasive solutions always seem to get suggested - e.g. GPS monitoring of mileage, or pervasive license plate tracking etc...
That will become a problem in the US as well, since US highway construction and maintenance is mostly funded from motor fuel taxes.