There are some good arguments against that. It creates a deadweight loss by banning high utility private uses of the car (driving kid to hospital) and instead there would be an increase in low utility "work" uses of the car (delivering a single banana to a bodega). There is a parent out there who would be willing to pay $X to drive their kid to hospital, and a work vehicle user who would forgo paying $X by staying off the road, but under a blanket ban that won't happen.

It would also increase the incentive for people to play games like claiming their personal car as a "work vehicle", throwing a little advertising decal on the side, things like that.