Many third-world countries already have this—usually fleets of young men on motorcycles that will deliver whatever you need.
Back then, mail could be delivered same day within a city.
One very memorable experience I had was sending a check in the mail to London, from Edinburgh, in the morning, and then receiving in return the ordered merchandise in the evening of the same day!!
[Those two cities are very major destinations and so mail between them is presumably well-optimized, but I was pretty flabbergasted that this was possible...]
Incredible connectivity!
next-day delivery within nyc is pretty much de rigueur.