We're already a few decades past the point that you've described. Email has been the biggest social network for a long time, dwarfing Facebook and any of its competitors.
Basically all Facebook users have at least one email account. Then there are all of the people who don't use Facebook, yet still use email. That's a lot of people!
Also, that's really only just considering personal email usage, too. Many of those people, whether or not they use Facebook, use email as part of their jobs.
Maybe Facebook or some other mechanism will catch up with email at some point, but that's looking very unlikely.
Email is broken for a lot of reasons. Managing your contacts, finding lost contacts, finding the email of that person you met last night, party planning, birthday reminders, attachments, sharing photos with groups of people.... There are a lot of things that are extremely difficult to do with email, but are very easy to do on Facebook. So I consider Facebook to be simply a better email client for communicating with your friends and family.
A next-generation email/facebook/social system will have to take things to the next level, and integrated with your phone, and perhaps even replace the conventional cell phone carriers completely.
Basically all Facebook users have at least one email account. Then there are all of the people who don't use Facebook, yet still use email. That's a lot of people!
Also, that's really only just considering personal email usage, too. Many of those people, whether or not they use Facebook, use email as part of their jobs.
Maybe Facebook or some other mechanism will catch up with email at some point, but that's looking very unlikely.