I think the main reason is simply to get people to invite their friends to the site, thus increasing the number of users via peer pressure.
For specialty social networks (or specialties within a general social networking site), your friends are probably not the best people to connect to. In that case, it would probably be better to use unidirectional links so that you can "subscribe" to anyone whom you would like to learn from.
Yet these unidirectional links -- while better suited in such cases -- are not great in attracting people to the site. And so such sites probably won't get enough critical mass to be interesting.
It seems to me that friend requests should act as subscriptions. They could then be upgraded to bidirectional links if the friend request is accepted.
Moreover, such links should not designate friendship at all, but rather, interest in keeping in touch with someone's activities (e.g., their subscriptions to groups, the apps they add to their profile, etc.).
You could use some sort of reward to encourage people to invite their friends that has nothing to do with these links.
