Several of my friends had multiple accounts for exactly that reason. Not so much CHEATING at Farmville, but one account for games, one account for everything else, to keep down some of the spam to their personal feed.
There’s a Catbook app (with variants for basically every beastie I’ve ever seen kept as a pet, including rodents and ferrets) for those doing “pet pages” tho. Much easier than a separate signin.
The time to deal with this was years ago. But then again, had FB required ID verification from day one it would never have been a technology leader. Openness, flexibility and anonymity are all part of the FB "special sauce." You can't pull them out now any more easily than you can pull the wheels off a moving car, and not withut similar results.