Craftsmen are private citizens too, their vehicles are their personal property. Many delivery drivers are also owners of their vehicles, and do delivery on contract. Not everyone is employed by huge corporations who got exceptions.

We (me and my wife) were just renovating an apartment in a city center, where the traffic limits apply. The problems the craftsmen had are real, and I speak from my own experience. Many times the solution was be bold and hope cops will be sympathetic. They were, though we got the recommendation to sell everything and move somewhere else, where there are no such problems.

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?