The drone could hover over the sidewalk in front of a building, you could signal it with your smartphone similar to how the sign is used in the first video. The drone could then drop the package or it could have a mechanism that allows you to pull the package from the drone while it's in the air above you.

Heh - have you ever been close to a quadcopter capable of carrying a 2lb payload for 20+ minutes?

It's pretty much 4 carbon fibre lawnmower blades thrashing around in the air. I'm not getting anywhere near close enough to remove a payload from one while it's attempting to keep a stationary hover in an area of poor gps reception.

I'm reasonably careless with my little quads (~350g with 5 inch plastic props spun by 220W motors), but my medium sized one (~800g) gets treated with much more respect. I've got a friend with a 5+kg Octocopter - it's got 2+kW motors spinning 18 inch carbon fibre blades, I don't get within 4 or 5 meters of that when it's powered up and armed (and I'm extremely wary of it when it's got power connected but isn't "armed", because that's really just trusting Chinese electronics and open source software to not chop my fingers off...)

I admittedly haven't been that close to one but we do trust or are seriously considering trusting software to control heavy machinery like cars. Is is truly so out of the question that we might be able to make them safe enough for that?

It might require more advanced designs, far better tested and well regulated software but being able to get that close to a drone would enable a lot more use cases for them. I think many people are going to invest quite a lot of money into making this possible, so I think we're going to see something like this eventually, even if it takes decades.

You can mitigate this a lot with more props of shorter diameter moving slower, and grilles to serve as prop cages, at the expense of somewhat lower flight efficiency.

Good point, but Amazon's drones are probably going to be propelled by ducted fans for just this reason.