With that said, I understand the larger point you're making about government surveillance. I just don't see most people being able to opt out of Facebook. Moreover, the government can compel Facebook to hand over whatever data is provided by users voluntarily, making the private/public split less than airtight.
Remember a few years ago (maybe even 10 years now) when facebook started testing their facial recognition capabilities? You'd post a photo, and it would highlight all the faces, tell you who they were, and ask if you wanted to tag them. It likely has a photo of 99.99% of living people at this point, and has profiles on them, cross-linked with any relevant discussion people have had about them (even if they're not on facebook).
Any site that allows you to "log in with facebook" is running their analytics which tracks you across sites, and builds your "profile", and if you have a gravatar on one of those sites, there's a good chance Facebook can now associate you with any photo that has been uploaded of you, even if you just happened to be in the background.
People were writing about this stuff in the '80s; it seems like some don't realize we're already there.