I think you still want a vehicle weight multiplier. A Hummer pays more gas tax than a Civic because it is heavier and uses more fuel, so covers extra road damage. A Hummer EV is going to cause more damage than a little Renault Zoe. I think it's appropriate(and a bit of a motivator) to charge the heavier vehicles more.
I don't think you need to worry about border crossing vehicles. It all kind of works out in the end. Only having access to KM totals, not location info would be ideal for privacy reasons.
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