Maybe this can be efficient if the drone had a fixed wing so it can glide. Or we can make the "structure" really really tall -- perhaps the delivery plane can launch drones that basically paraglide into the city below, and the drones can fly back to a collection center once they've delivered the payload.

Alternatively, you could use a ground-based slingshot to vertically propel gliders, an approach that is already used in the military and for some long distance UAV testing. However, the wing-based UAV vs. rotor-based UAV physics are very different. Landing an elevated glider with a clear path to its target is one thing, maneuvering between trees and power lines in a complex environment without rotors is quite another.

Then you need to look at a 'convertible' UAV with both features... undoubtedly this raises the cost, reduces the carrying capacity, and is already being pursued.

Finally, you could zoom out and re-evaluate the business case. Why not use a network of local dispatch points (handover points to ground-based UAVs or vans) to reduce the distance to the consumer and with the smaller geographic scope negotiate private airspace access on locally agreeable terms. I believe this is the future for general consumption (food, regular deliveries within small package weight/dimension limits).

Wouldn't the cost of elevating the loaded drones to the rooftop of that tall structure negate any monetary gains? Wouldn't the cost be exactly that of simply using grounded vehicles that elevate themselves?

(edited for clarity)

In summary: Rain the deliveries onto the neighborhood with a railgun.

In real terms, I'm doubtful that the majority of people's goods would withstand that kind of rapid acceleration. Consumer electronics frequently break from hitting the floor, a rail gun would probably shred them. You could accelerate more slowly, but then you need more runway, and you might end up building a skyscraper anyways to get a delivery radius that's more than half a mile.