Those schlubs do require a current DOT card and fall under DOT driving regulations and limits and have to maintain a clean driving record. (i.e. 60 hours per week max, no more than 14 hours in a single day etc.) And they are monitored like crazy. Seatbelt buckled when moving, back and interior bulkhead doors closed, backing too much, total distance driven during the route (and compared with the computer estimated route and times). And let's see that drone deliver 60" flat screen TV's.
I drove for UPS this last holiday season, and I really doubt UPS is at all worried. The amount of volume a single schlub driving a package car can deliver and pickup in a single day is quite surprising. The swarms of drones that would be required just for smaller packages would be overwhelming, let alone being able to handle large and odd shaped packages, envelopes and large volume deliveries and pickups.