This is clever gamification but probably most of the players would be the suburban and rural poor, for whom excess driving is more likely to be non-discretionary and the only option for local + regional travel. The effect would be to limit their quality of life, either by deferring access to money for basic expenses, by limiting access to employment, or by discouraging children's access to recreation and socialization opportunities. There are similar arguments against VMT taxes

How about we tax cars as property, based on Blue Book value and modulated by income bracket, and maybe even by specs like weight and fuel economy? Some states are already doing at least a basic version of this. And instead of giving the money back, we can fund fare-free municipal bus and rideshare programs