If you have a few packages in your car, each worth a few hundred bucks, you're not significantly more risky for the company underwriting your insurance policy.
So I doubt that a commercial policy for parcel delivery is going to be much more expensive than a personal policy. It's just that the driver would need to get one.
Also, a company like Uber or Fleetzen would be able to keep it cheap by insuring all of their drivers, who would be screened and immediately fired upon having an accident.
When you have a personal policy and never get into an accident, your premiums stay really low. It's when you get into an accident that they skyrocket because people who get in accidents tend to account for a disproportionate share of total accidents. Put another way, if you have never been in an accident, you're unlikely to ever been in one.
Uber and Fleetzen would immediately remove accident-prone people from the risk pool, which would keep the premiums down.