I do not understand this obsession with adding an exciting new tax/fee/whatever when we can just raise the damn gasoline tax. Yes it's regressive, but no more regressive than a per-mile fee. The incentives are roughly correct - big vehicles with bad MPG ratings that damage the roads and climate more pay more.
It's easy to collect a gas tax. There aren't a hundred million gas stations. A mileage tax has to be collected on every car owner. And there has to be enforcement. And collections. And punishment for nonpayment.
Increase the damn gas tax.