What compelling State interest requires the State to know anything at all about the mileage you freely choose to put on your car?
What right does the State have to say you cannot "tamper" with anything that is your own property?
Knowledge is power. The less the bureaucrat-tyrants know, the better. A lack of a freedom to move...is a lack of freedom, period.
The same compelling interest the relevant billing entities have in knowing how much electricity or water you use. Like electricity and water, road maintenance costs money, and unless your car flies to its destination, it imposes wear-and-tear on roads, which directly affects maintenance costs. Maybe you'd be more comfortable having roads maintained by some private entity (and that would be fine by me), but the bottom line is that somebody needs to pay for road maintenance, and odometer readings, which are taken during annual vehicle inspections (in states that have them) are a reasonable way of finding out how much wear and tear (and therefore cost) a given car has imposed on the roads.