Let's say they somehow manage to perfect street landing, so that drones won't come crashing down on people, parked cars, construction sites etc, independent of weather conditions (snow, ice) - what happens then? Does the drone wait until you go down and pick up your pizza? What would prevent people from stealing a (rather expensive, I imagine) landed drone?
Does it just drop the deliverable from a safe distance? So what about "oh hey, there's a hovering drone, let's go pick up some free pizza".
Still lots of ways for things to go wrong, but I bet there are some interesting solutions. It's all very new.
Or, hey, as long as we're spitballing, what if it were common to have some sort of household bot? A butler-bot, if you will. It might have the responsibility of ascending to the roof (via some sort of track) to take delivery. You might need some sort of defenses against burglar-bots but ... I think I'd better stop here. ;)
There seems to a bunch of seemingly plausible ways to do this, but the first group to work on the problem will surely solve it then patent the method.
I.e. where does the drone land? How does the recipient pick up their package? What if you live in an apartment, how do you get your pie?
This make me think drone delivery is probably waaay more valuable in suburbia than a city setting. Delivery in the suburbia seems costlier currently (larger distances, lower densities so less stops per route, etc) and drones are well suited to deliver to a nice big front/back yard.
In cities - I don't see how they'll deliver pizzas, but maybe non-perishables can be deposited into receptacles on rooftops or street corners and picked up asynchronously.