I never said it was a sole source, but it is a large source (I thought the largest source). Do you have the breakdown of funding sources?
Most of your property tax (depending on state) is going to schools, not roads. For example, my school tax is about $3700 per year, while county tax is about $500 and local income tax is maybe $500. The county and local taxes support courts, parks, police, fire, public transport, etc. Yes, some does go to road maintenance, especially projects like bike lane and crosswalk programs, but that is relatively little. I pay about $400 per year in gas taxes, $90 in registration, and $90-120 in tolls each year (pre covid). Federal road money comes from a federal gas tax (not sure if there are other sources added since that was a big issue a decade ago).
Enforcement of the odometer reading might be tricky, especially at the state level for states without periodic inspections. It could work though. The reason I mentioned tires is because they are a consumable part and have treadwear ratings for how long they should last. It would be self-enforcing, to a degree, at the consumer level. Enforcement would be at the manufacturer or distributor level to collect the tax.