Well, as a literature lover and former literature teacher, I first reacted strongly. "What do you mean, why is it important to study literature?!" But I discovered that putting my thoughts and feelings into words was more difficult. So here, in somewhat random, conversational form, is what I posted to the list.
(This first is in response to the original poster's discovery that after reading The Second Mrs. Giaconda - which he hated - her son had then been very interested in an article about whether da Vinci had used Mrs. Giaconda as a model for the Mona Lisa.)
You commented that your son was interested in the article because he had just read the "boring book." But isn't that part of the point of education - to arouse kids' interest in areas they might otherwise never have thought about much? His life is richer (if only in a very small degree), and he understands more about Leonardo da Vinci, because he read that "boring book." Sure, it was hard to do - but if he has broader interests as a result, that seems like a worthwhile investment of time and energy to me.
Another reason to study literature - and one I consider critically important - is that it gives us a common frame of reference (both with members of our current culture, and more importantly with our cultural heritage). Reading Benjamin Franklin, for example, or Thomas Jefferson, or even Mark Twain, you'll find dozens - maybe hundreds - of references to literary sources, Shakespeare being one of the primary ones. Knowing the literature helps you understand what they're talking about.
I was just looking, for example, at Shadow of the Almighty, the story of the life of Jim Elliott (the martyr who gave his life to reach headhunters in Ecuador in the 1960's). His writing is scattered with literary references, and they tremendously enrich the reader's understanding of his life (and of what motivated him to give it to Christ).
Some of the most difficult literature to read (and I put Shakespeare in this category!) is some of the most quoted and has become part of our cultural heritage. How about this one: "All the world's a stage, and all the men and women merely players" (from As You Like It)? I'm racking my brain for the book I remember reading a while ago with a chapter title of "Out, Out -- " because it has a cultural reference I didn't understand at the time. In fact, the reference is to Shakespeare's Macbeth, which contains this amazingly thought-provoking section:
"Tomorrow, and tomorrow, and tomorrow,
Creeps in this petty pace from day to day,
To the last syllable of recorded time;
And all our yesterdays have lighted fools
The way to dusty death. Out, out, brief candle,
Life's but a walking shadow, a poor player,
That struts and frets his hour upon the stage,
And then is heard no more: it is a tale
Told by an idiot, full of sound and fury,
This section is even more thought-provoking if you know the Macbeth story - that it is spoken by a character who is responsible for murder, and shows the despair of someone who is caught in the grip of human depravity and can see no hope for escape. And all of this significance is built into the author's use of "Out, out -- " as a title for his chapter. Without the cultural reference, you miss part of what the author was trying to say.
I'm afraid I may have obscured my point in the quotes and illustrations. What I'm trying to communicate is that literature provides a reference point for understanding both our current and our historical culture. Even scientists use these kinds of references, almost without thinking, assuming that we all are familiar with them. They are found throughout news articles, magazines, history books - especially the rich writings of our forefathers throughout the colonial period, the 1700's, the 1800's, and even the first half of the 1900's. Only in the last 60 years or so, as our society became totally invested in the space race, did we abandon much of this heritage and turn our focus almost exclusively to science and math.
That said, understanding our cultural heritage doesn't require reading every single book on any particular reading list. Some books aren't worth the effort. What's important in high school, in my opinion, is that you get a solid grasp on a significant number of the works that have been foundational in building our culture. Shakespeare would certainly be included, but so would many other authors. Some are easier to read, some are more difficult. And some are only tolerable when you read them in a setting where you can discuss them - preferably with a group of peers.