I also have some familiarity with transportation infrastructure; unfortunately, we already effectively have a mileage tax - the major source of funding for roads are the federal and state taxes on gasoline and diesel (currently about $0.40 - $0.50 per gallon total), the more you drive, the more you pay. Supposedly, the increasing number of electric vehicles has the highway agencies looking at alternate sources of revenue. However, the primary driver for this funding search is more likely the increasing cost of new construction - an increase that is outstripping the annual increase in revenue from the gas tax.
I don’t trust Buttigeg (or anyone else) to come up with a good funding alternative. It looks like they want to tax miles by mandating GPS trackers for all vehicles (while keeping the tax on fuel at the same time). I don’t know what a good (or least bad) alternative would be. Some states are starting to supplement the gas tax with a sales tax, which, I guess, could have some rationale - as roads benefit the commerce that make sales possible.