A possible alternative would be to tax the electricity at the charger, but that also opens up more cans of worms.
Another thing to consider is that, beyond normal weathering, most road damage comes from heavy (and often overweight) trucks.
I don't see taxing electricity at the charger as being viable, because it's too decentralized. You can tax gasoline because it's distributed by relatively few places. You can charge a car off a normal 240V outlet (or 120V if you don't mind it being slow) so it'll be way too easy to dodge.
Tracking mileage and assigning to the state of registration might not be too bad. It won't be fully accurate, but the inaccuracies will balance out to an extent. Gas already suffers from this at a smaller level, since you can buy gas in one state and then drive a substantial distance in another state.
The fact that trucks are the ones doing all the damage is a big wrench in the works. Maybe the proper solution would be paying some by taxing truck mileage and making up the rest out of general taxes.