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There should simply be an annual fee based on vehicle weight and distance driven
Keep the vehicle in your garage and only drive a handful of times? Low fee, drive a monster truck thousands and thousands of miles? Large fee.
This also solves the problem of electric vehicles not paying towards road maintenance, as they are heavy and would wear the roads more than a standard vehicle that uses gas.
The problem is distance driven has a linear effect. The weight has an exponential effect. If you drive a monster truck 10 miles a year and you drive a shitty commuter that weighs 1/5 the amount 3,650 miles a year, the monster truck is gonna damage the road more. If the fee is anything but a 4 power exponent from weight and linear with distance then you're punishing miles driven more than they are contributing to road wear.
In fact the only time distance matters is if its 0 then why even bother licensing a vehicle heavy enough to be worth surcharging? If most people drive their vehicles more than 10 miles a year but less than 10000, you'd want the fees to scale with normal use cases rather than some fringe use cases that encourage people to own vehicles they never use.
Edit: The way to do it is probably surcharge people for the weight of the vehicle + the weight of the gas the vehicles use in a year.
You can have tiers to solve that, like vehicles under 5000lbs pay $x per kilometer driven, vehicles between 5000lbs and 10,000lbs pay $y per kilometer driven, and vehicles over 10000lbs pay $z per kilometer driven.
Wouldn't be perfect but closer.
My preference would be to assign an equivalent single axle load to each vehicle based on make and model or avg trailer load capacity and then scale that linearly with mileage.
https://pavementinteractive.org/reference-desk/design/design-parameters/equivalent-single-axle-load/