I wonder if some kind of weight + mileage tax would work better?

Ultimately I don't see how one could institute a fair system without converting all roads to toll roads (perhaps with variable pricing to manage demand).

Gasoline taxes are a reasonable proxy for "usage", so heavy users contribute more.

Registration fees treat everyone of the same make and model the same, be it a livery vehicle with six-digit annual mileage or a proverbial old-lady whose car is being driven around town twice a week. And one can't exactly levy a tax on kWh.

(This is bad because it makes driving more very cheap for people who already have cars, the exact opposite what's good for extracting maximal utility out of minimal fuel use)

The high taxes on cars and gasoline usually goes to improve public transport.