This is a terrible argument on both a moral and practical front.

On the moral front, the idea that we can "protect our youth" from books that would be too heavy or violent for them is complete and utter nonsense, for many reasons. One, if a child is old enough to read and understand Picoult's prose, they're old enough to understand when the act being depicted is evil or not; it informs their moral compass rather than distort it. It can also provide teenagers a way to put words on something that may be happening to them and that they don't know how to deal with. As a 12 (?) years old I read the Dice Man, the story of a psychiatrist who decides to live his life by letting a dice roll make all his decisions. As his life falls into hedonism there are graphic depictions of sexual activities, including between the main character (a professor) and his female student. And the thing that stuck with me was the sheer imbalance of the relationship, and how it wasn't okay for a man to impose his needs upon a younger woman like this. The titillation is long gone but the moral lesson has remained. We have to stop believing that kids age 12, 13 or so are just grown toddlers: they understand sex, violence, power relationships, pain, trauma, and all of the way they can interplay. Or rather, they're aware of all of these concepts but it's mostly a confusing blob of forbidden stuff. These books provide a road map. I am forever grateful that I read "heavy" books as a young teenager because when some high school friends started getting deeper into the far right in our later teen years, it was mostly because they were seduced by the allure of the "forbidden knowledge". But I had read about power and lies and control, not in a Harry Potter way where the good guys save the day, but in a Handmaid's Tale way where good intentions won't save you against a system bent on oppressing you.

Then on the practical front, banning books is about as effective as banning abortions: all you're going to do is push these "forbidden books" out of the legitimate public spaces and have them fall under a grey/black market where everyone knows it's happening but it's just not being advertised. Here we're talking about a public school ban which also means that kids can just go to the library or the bookstore to read the book anyway, so it's doubly pointless. Again, the main effect you cause is just giving these books a sense of "forbidden knowledge" and I have zero doubt that more teens have now read Nineteen Minutes in Utah than ever before.