The problem with this is that the user will be presented a giant list of several hundred friends, which is intimidating to say the least. (Facebook hasn't really tried to discourage indiscriminate friending, preferring instead to algorithmically filter what it shows you in your feed, with the result that most users have ended up with an out-of-control friend list.)
There's one and only one way to make this work with an already existing social graph: show the user a clustered view of their friends. To see examples, do an image search for 'vizster'. http://vis.stanford.edu/papers/vizster
"Facebook hasn't really tried to discourage indiscriminate friending..."
This is certainly the impression I've got, though when I first signed up, it would ask you "how you knew" somebody, and if you said "I don't know them" then it would disable the continue button. That's something.
In general though, the more people add friends, no matter how trivial, the more information Facebook has, which is why they don't explicitly discourage friending less-meaningful relationships. So even if you probably won't talk to Bob Smith more than once a year, it's still valuable for Facebook for you to add that connection and let it rot: that's added value for them.
So then Facebook's value is more in being an address book rather than a social network. Google out-social'ed Facebook with Google+ with Circles and Hangouts, and everything else.
There's one and only one way to make this work with an already existing social graph: show the user a clustered view of their friends. To see examples, do an image search for 'vizster'. http://vis.stanford.edu/papers/vizster