As with you folks, I'm concerned about the privacy issues. Pretty much anything other than a yearly odometer check is much more granular than I'd like the .gov watching my travel.
I think this would also be a pretty hard sell politically right now, as it's a pretty regressive tax, and all the usual suspects will come out of the woodwork to describe how it's racist (because poor folks have to pay it), Sexist (because it would hit single moms), probably white nationalist (gonna tax indigenous people to drive on the land you stole) and whatever the hell other tribal group doesn't want to pay. Gas taxes were passed and accepted before today's toxic mix of intersectional specialness took over everything.
Can you imagine the caterwauling if they tacked on an extra 30 cents or whatever per mile to and hit folks with that? Why AOC's mom wouldn't have been able to drive to the Hamptons and clean mansions.