You're operating on the premise that facebook.stackoverflow.com != stackoverflow.com.
The questions on facebook.stackoverflow.com are a subset of the questions on stackoverflow.com. If a question appears on facebook.stackoverflow.com, it appears on stackoverflow.com.
The users on facebook.stackoverflow.com are a subset of the users on stackoverflow.com.
So, aside from the premise being flawed and it not happening, what good would this do? All it would do is hide questions from experienced users that need to see them in order to self-police the community. The questions sitting around and not getting dealt with would not improve things. It wouldn't educate new users.
The same quality checks and question/answer blocks that exist on stackoverflow.com exist on facebook.stackoverflow.com - because they are, at the root, the same site. Downvoting, flagging, and voting to close is the appropriate action, just like on stackoverflow.com proper.