Since there is no answer, let me try to provide one:
First, the two misconceptions in the OP:
Movies need to be rated by MPAA.
Not true, this is a voluntary process. From the Ratings guide:
WHAT IS THE PURPOSE OF THE RATING SYSTEM?
Movie ratings provide parents with advance information about the content of movies to help them determine what movies are appropriate for their children at any age. After all, parents are best suited to knowing each of their children’s individual sensitivities and sensibilities to pick movies for them. Ratings are assigned by a board of parents who consider factors such as violence, sex, language and drug use, then assign a rating they believe the majority of American parents would give a movie.
DO ALL MOVIES HAVE TO BE RATED?
No. Submitting a movie for a rating is a voluntary decision made by filmmakers. However, the overwhelming majority of filmmakers have their movies rated, and each member of the Motion Picture Association has agreed to have all its theatrically released movies rated.
What's more, the age rating is not legally binding (with an exception for obscenity - in many places worldwide it is illegal to expose minors to overly sexual material), so if a movie theatre owner will let your kid watch R-rated "The Passion of Christ", there is not that much you can do (I've actually seen people encouraging their children to see it "because it is religious").
However, if the theater sold you a ticket to an R-rated movie, even though you're under 17 and not accompanied by an adult, then you have a right to be there. If you are removed, the theater will likely have to refund your ticket.
There are no agencies that rate books
As @GarethRees pointed, there are such agencies, for example Compass BookRating:
Compass Book Ratings provides a standardized rating system so everyone can more easily evaluate their reading options. These book reviews are for parents, teachers, librarians, readers, and anyone looking for a book that best fits their preferences for story and content.
Again, their purpose is not to enforce some legal control, but to provide easier guidance system.
Of course, there is quite a long list of books banned by the various government at various times. The reasons also vary - from "obscenity" (The Decameron, Lolita, 120 days of Sodom), through religious (The Satanic verses, Quran) to political ones (Mein Kampf, The Protocols of the Elders of Zion, Catch-22).
But if we get back to the age rating, I think it boils down to the old saying "The picture is worth thousand words": It is easy to look at the picture and see all the gory details, getting all that just from plain text is not as easy and strong. I can write "the executioner cut Jane's head off; blood splashed on the onlookers" and no one would probably think twice about it (ok, it might not look good in a kids book but even then there are exceptions - some old nursery rhymes are much creepier than you think), but if I'd try to draw it or show it to on a movie... Which is why you will notice the age suggestion more often on a graphic novel
than on a book: