The bigger impact would be on smaller retailers, that don't have this service. This service is an absolute killer, making it faster to order a toothpaste from Amazon compared to picking it up at a shop outside your house.
This would be an incredible benefit to human economy. Imagine the millions of retail jobs completely obsoleted by drones. Consider the price difference between wholesale and the corner retail shop -- a cost this could largely eliminate. Consider all the hours wasted in retail-facing interactions.
If my local mom-n-pop store has an app and a drone, I would shop there.
1) Scale: a small store might not have enough sales to justify buying a single drone and training the staff to use it.
2) Regulation: licensing and certifications to be allowed to use these - particularly in a completely hands-off way - may have high fixed costs that a small store can't afford.
3) Lack of knowledge: most small store managers probably don't have any idea of how to set this up, or that it is even possible.
And in the end, why would you buy from the local mom-n-pop store? Nostalgia? Helping the people you know? I think that'd wear out pretty soon or just not work for many people.