most of the traffic near city centers are not residents but commuters and shoppers. the goal is not to decrease the number of miles driven but to decrease the number of cars in a zone.
Agreed that pay per entrance is easier to do and works well for creating the right incentives around modeshare, but VMT taxes probably have their place too as a means of funding road infrastructure (which gas taxes ostensibly do now, but poorly, and not in a way that accounts for EVs well). More precisely, you'd probably want to tax vehicle miles traveled per unit of vehicle weight, to charge more to trucks (which cause increased road wear, and pay more under current schemes due to increased fuel consumption).
most of the traffic near city centers are not residents but commuters and shoppers. the goal is not to decrease the number of miles driven but to decrease the number of cars in a zone.