And thereby totally removing the point of engaging in Social Networking. Plus, the second you post something you'll give the game away to those on your friends list who actually know you, triggering all the questions of "[name] why did you change your name?" Plus, the only people who'd want to be anonymous on Facebook are haters, trolls and stalkers.
How about set up privacy settings that restrict total strangers from viewing and just be done with it? Or how about don't post anything ridiculous to start with?
The reason for the post is exactly for people who may never post anything, but may still want a Facebook account to privately message friends or just keep track of what others are doing.
If you don't want to be fully anonymous its quite simple to skip the name and photo changes and dial back a few settings. Hopefully by showing people how to go the most extreme, they can decide for themselves what they want their settings to be, since all the relevant settings are now easy to find.