Every car has an odometer... one could think of a relatively convenient scheme where you can get your car inspected once a year at any refueling station, and tampering with the odometer is a crime. Won't stop everyone, but does it matter?
How do you distribute the money to places where people drive but don't live? Gas tax handles this to an extent, but milage tax wouldn't; not without border checkpoints or mass surveillance.
To give an example - in my hometown in a few places there are small wires on the road surface that measure the number of cars that drive over it. Private by default!
I was being slightly facetious in referencing tyre size, although people regularly have to adjust speedo/odometers by 10% or more when fitting large tyres on off-roaders.
Odometers can have their values changed at will, at least in ICE vehicles, often for valid reasons.
New Zealand collects road tax on diesel vehicles using odometer readings. It generally works for heavy commercial vehicles where the owners have more to lose risking fraud but I know private vehicle owners who would wind back or disconnect their odometer to avoid the tax.