When you consent to something such as this, you are more than potentially violating the privacy rights and expectations of those with whom you've communicated via Facebook. How many people have sent you a private message? Your profile may be wide open, but most people do not expect that what they've asked you to keep private would be handed over to your prospective employers, etc. If you can't keep such things private, why would any prospective employer expect you not to leak the employers proprietary information, such as say private-customer lists?
What if you have communications that explain your deepest ideological and/or religious beliefs and are not hired after exposing those to the prospective employer at the employer's request? That employer could be sued. The burden of proof would be on that employer, as most employers are forewarned not to ask about race, religion, or political affiliations, etc.
The world just becomes a harder and harder place:
When Justin Bassett interviewed for a new job, he expected the usual questions about experience and references. So he was astonished when the interviewer asked for something else: his Facebook username and password.