Terrible idea. You'd need a new layer of bureaucracy to implement it
Not really, not if it's used to fund local roads and a cap is established on how many miles are taxed. Most, if not all states require you to pay property tax on cars and the county sends you a bill based on the blue-book value for having been driven so many miles (in SC it's 15000 mi/yr) with a way for you to appeal the bill if you've driven it more than that so that it has a lower value. Set the tax based on the assumption you drive the vehicle 10000 mi/yr and let people appeal it if they can show they drove less. Other than you'd get more appeals thus making that layer of the bureaucracy bigger to manage the increased workload, there would be no real problems.
As a replacement for the federal gas tax this wouldn't work, but for state and local gas taxes it would.