You sure write alot for somebody who doesn't know anything about the service. I don't 'use' foursquare either, but I've tried it and know what it's about.
A single network wouldn't be successful in building a foursquare competitor, as not all of your social contacts are on the same network.
Part of the value of FourSquare in the long term is to be introduced to new places (likely around the world) where your social network has checked in and found value. A great restaurant, coffee shop, attraction, etc.
In addition, there is the game element, which apparently people find fun, but how much fun is a game you can only play with people on the same network? How successful would skype have been if you could only speak to other people who already had skype? That is basically what you are proposing.