The gas tax is $0.30 per gallon. Instead of paying that $0.30, I can choose to pay $0.015 per mile traveled. Paying per mile, I can only go 20 miles for $0.30. Unless I drive a gas guzzler that averages less than 20 mpg, I am being taxed more.
Plus this removes one of the benefits to driving an efficient or alternative fuel vehicle.
Plus (as many prior posters have pointed out), weight of a vehicle is proportional to the amount of road damage it causes, and would be a far better metric for assessing taxes to repair roads.
Dumb.