True, a personal vehicle weight registry and fairer tax application would make sense. A couple issues though.

Commercial vehicles do way more damage than most cars and light trucks to begin, charging them in the cubed level would constrict an already underpaying industry (but might actually encourage more rail delivery).

Second since the main question is for parking, enforcing weight based fees would be expensive, where a large scale would be needed at the entrance and your local weights and measures laws may apply. Length based could be enforced with just one employee and a $5 measuring tape, if you didn't want to deal with automated sensors which would still be less costly to install than weights.