Alternatively, if the monetary value of the network is defined by the edges, rather than the nodes, and everyone is connected to everyone else, how do you determine the valuable connections from the meaningless ones? As the number of connections goes up, their individual value would seem to go down. Beyond that being basic economics, you're setting yourself up to be limited in the kinds of additional things you can do as the meaning behind the individual connections approaches zero.
If twitter added some metadata behind the ability to create connections, like allowing users to group their connections into buckets (initially preconfigured to encourage meaningful use) like "co-workers", "friends", etc and let you filter what you publish and what you subscribe to in different ways, it could work. But then they'd have created FriendFeed.