Since usage damage to roads is directly connected to vehicle weight, why not eliminate the fuel tax and replace it with a pure weight mile tax? Meaning that you pay a cost per mile driven, per pound of gross vehicle weight. Odometers would be checked during annual or biannual vehicle inspections, and the tax would be assessed as part of vehicle registration.
The state of Oregon has a version of this for EVs currently. You can either pay an EV registration surcharge or you can opt to pay per mile. Last time I checked, if you drive less than about 6,000 miles a year, the pay per mile option was cheaper. If you only drive in Oregon, you can use the odometer, if you drive out of state and don't want to pay for non-Oregon miles, you sign up with a tracking service that monitors if you are driving in or out of state.
We already do a version of this for big trucks
Yes, there would be privacy concerns with various implementations of a weight mile tax in cases where the tax rate might vary based on where you were -- such system would require tracking. But if you drive around with a cell phone, you are being currently being tracked, and many (most?) modern cars are already collecting and reporting location information.
A weight mile tax (as a replacement for all other fuel or other "special" vehicle class based taxes), would be fair and appropriately spread the cost of road maintenance out to those who use the roads. It eliminates politics about fuel sources (at least with respect to taxing for road maintenance).