Where I am currently we go through a brand new set of Michelin tires in a year and a half (less than 30,000 miles). That's because the roads to/from our home are very windy. You would also be encouraging government to make their roads more abrasive and the theft of tires to avoid the tax.
Like I said, far from perfect, but better than a gas tax.
If you're going through tires because the roads are windy, that also means you're wearing down the roads faster than if they weren't windy. Or you're buying Michelin (I don't know how they are these days, but 20-odd years ago when I paid close attention those things lasted about half as long as a Tiger Paw, though you could increase their lifetime significantly by idling away from the tire shop).
A theoretical increase in tire theft to avoid the tire tax would be offset by a theoretical decrease in gas theft to avoid the gas tax.
Like I said, far from perfect, but better than a gas tax.