Well, with electronic toll-paying that could work, but it would still shift the burden from low MPG to high MPG cars.
The great thing about a gas tax is that it's a simple way to kill two birds with one stone: encouraging higher mileage and paying for infrastructure. The problem is that not everyone agrees that both birds are important. Two-birders think that high mileage vehicles should be discouraged because of externalized costs -- pollution mainly, but also space required in parking lots, greater risk to other road users etc. One-birders don't care about externalities but understand that the roads and bridges need to be repaired. Zero-birders are just idiots.
I'm a two-birder myself, so raising the gas tax is a no-brainer. I'd also issue everyone a flat rebate per driver, because in fact I'm a three-birder: I'm concerned about the effect of a regressive tax on the working poor who have no options but to drive to their jobs.
But I'm also a realist. There are a lot of one-birders out there and the roads need repair. It's also politically easier in one-birder territory to sell something as a fee rather than as a tax, even though from my perspective that's an irrelevant difference if you're raising the same revenue either way.