That gets tricky though, Can tradespeople can use their vans to do their food shopping? Can private citizens become a painter/decorator so they are then allowed a vehicle? Can a private citizen have a vehicle if their sister is disabled?
Government can issue permits, on request. If requesting a permit can be done through an app or website, then this could even be feasible on a per-case basis. E.g. plumber needs to visit the city, requests permit, then drives to client.
Doesn't have to be expensive or time consuming, could be something you fill out in 10 mins and drop in the mail/submit online. IRS already knows you are an independent contractor so that could be your verification right there.