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.
Instead of friend requests and acceptances, users should just be able to subscribe to other people via unidirectional links.
Such unidirectional links don't designate friendship at all, but rather, interest in keeping in touch with someone's activities (e.g., their subscriptions to discussion 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.
For example, wherever people are listed throughout the site, you could rank them based on the number of friends that they have invited to the site.