The "social web" is no where near as important as search. Imagine removing search from the net. Now imagine removing Facebook or other social networking sites. The difference is staggering.
Social websites, widely, are websites that allow users to connect to each other. Even 4chan is social. Without search, we couldn't find anything on the web, but without social we couldn't talk to anyone. I don't know which is worse, but they would both be enormous losses.
Facebook, or "the social web" as its coined these days, is about the friend graph (ditto with twitter - its about who you follow, and who follows you), not about discussions.
Imho, the web will function perfectly well without facebook - each of the features of facebook such as photosharing, event organizing etc, all have ready replacements. Sure, the friend graph helps you connect easier/faster, but taking it away isn't as detrimental as taking away search.
Facebook wants to portray itself as a one-person-one-account service, but the lack of extra accounts is largely because they've obsoleted most of the reasons people would create multiple accounts.