You are right. Damage to the road goes up by vehicle weight to the fourth power (!!!!!!!). Texas reg fees are according to vehicle weight (but I don’t think to the fourth power, though).
The 18 wheelers and other heavy vehicles cause the pavement to flex and bend, causing internal cracking.
If 18 wheelers were taxed to the vehicle weight to the 4th power, our groceries and other trucked-in goods would be much higher in price.
Just put a card swiper in the cars. Before we can drive we have to pay our good citizen tax.