Here's the plan: you and 5 people closest to you move to the same area. Then each of those 5 people moves 5 of their closest people to the same area. Repeat ~13x and we can all finally be together.

Unicity? Because this will be the only city in the world :)

Or not "the City", but "THE city". I am failing to come up with more ideas, maybe we need help from some crack marketing teams

So if a mega-city had a billion people. Maybe that's too much, let's say a 100 million people. Let us say this may be possible this century with some innovations in our habitat. So with a 100 million people in this mega-city, how many people can actually live close to each other? Even if you go 3-dimensions (connected skyscrapers), not sure this model will bring people close. Will it?