Facebook – Purpose of Poking

First, Facebook as a whole is more valuable if it maximises user volumes. So they're never going to stop wanting you to add that new friend from some other address book.

Second, the Facebook experience is pretty lame if you have only a few Facebook friends. So creating a new link may be a marginal value gain for you, but it may help the other party get into the sweet spot and become a regular and committed user.

More speculatively, Facebook ads themselves seem (from what I get offered, anyway), pretty feeble, so maybe there's an element of Facebook improving your general perception of the right-hand column by sometimes not even showing you some horrible, mis-targeted ad and just doing self-promotion, not caring all that much whether you respond. In this case, you've responded indirectly by talking about Facebook, I'm making a mental note to see if I am getting that same treatment, and we're both even more bought into the idea that Facebook is an unassailable, valuable site in a way that Myspace and other toppled social media towers must not have been!

I'm not sure the second part of the question question makes sense...

If you think of Facebook connections as ever-widening circles, you have:

• Yourself
  • Friends
    • Friends of Friends
      • Strangers

You want to reduce the "can send friends request" to "narrower than 'Friends of Friends'", right? But if you look at the hierarchy above, exactly who would include? Either "some" Friends of Friends, which Facebook would need to know how to narrow to "some", or just to "Friends". If the latter, well, Friends don't need to send you a friends request, true?