I'll give you the non cynical answer: the funds wouldn't go to the right places because you'd have no idea where the driving happened. So your home state gets paid for you to drive all over the country on a cross country road trip.
That’s the current situation with the gas tax. Why are we trying to change it? Right now road usage is calculated based on observations made of the roads in question. You deploy some method of counting cars over a period of time and then make your estimates. Why do we need perfect surveillance when a rough count gives us all the data we need to know to determine service schedules? I’d bet that the current methods also cost a fraction of the amount it would to develop multiple apps plus car integration plus reporting systems plus training and salaries for the people that now manage that data and the ongoing maintenance of the apps and infrastructure. I’d also bet all those new costs would be pork for someone’s district.
I would be surprised if the numbers were that different, especially with aggregations at the state level. Each state has people who drive all over the country. Each state has people who only stay local. If we were going granular, at like a county level, tourism to low population locations like the Grand Canyon might need to be accounted for, but states encompass enough area and people that just taking the total for each person in a state would probably be accurate enough.
Is 100% accuracy necessary? Why not try a much cheaper and less invasive option before panopticon?