It is time to revisit the question of the purpose of education; is it to get a score on a multiple choice test or to impart the ability to think? Great literature not only entertains, it teaches life skills, values and how to question.
Just like math is not about arithmetic, but a thought process.

I taught 7th grade English for 35 year & have seen the decline of literature in public schools first hand. I attribute this to Bushie's No Child Left Behind, which changed the emphasis in English education from knowledge to skills. Our district curriculum coordinator referred to our classroom materials as stories, not literature. All she cared about was whether our students had the skills (her word) to score sufficiently well on the PSSA's. So instead of literature we read mainly brief passages written by hacks as practice for those all-important tests. (I ignored her edicts as much as I could.) Taking anything of lasting value with them from my classroom was immaterial to her. Skills be damned! A trained monkey can acquire skills. We need to help our children acquire knowledge & an interest in learning. Good literature, well taught, can accomplish this. I've always said that I have learned more history, psychology, & sociology for literature than I ever did from a textbook. And, I'm still learning.

There is hardly a clear lack of emphasis on literature in K-12 education, relative to other subjects. It is my experience that literature is over-emphasized, and more important topics in reading and writing are de-emphasized as a result. I strongly suspect that the literature teaching establishment is designed to be self perpetuating more than it is designed to be efficient. And, it tends to turn entertainment into drudgery, turning people off to literature.

Many people learn and remember most from personal experience, stories, and anecdotes. The value of literature is that it can teach truth in a memorable way. However, there are two major problems with literature as a tool to teach other subjects.

First, literature is fiction, and it can also teach lies in a memorable way. In general, the lies are more dangerous than the truth is valuable, largely because it takes more effort to negate an established lie than it took to put it there in the first place. (During WW2, Gen. Omar Bradley observed that it took longer to properly train a division that was badly trained, than it took to properly train a new one from scratch.)

Second, literature tends to be inefficient in that a reader's time is spent mostly on the story, rather than on specifically understanding the message. To the extent that the reader's time was intended to be entertainment, learning is a bonus. But, a student's time dedicated to learning is usually far better spent with nonfiction.

The ability to read, understand, and write non-fiction is far more important than the same for fiction. It is critically important to for readers to sort out truth, lies, and omissions. Nonfiction writing skills are almost equally important, for the ability to communicate clearly and efficiently, and also as an aid to identifying poorly written nonfiction. Much nonfiction presented to the public does contain serious lies and omissions, and it takes a lot of knowledge and skill to sort most of this out, yet little emphasis is spent on this in K-12 schools.

I certainly agree with Robert Becker's comment about the importance of understanding the context when reading the classics. Without that related understanding, the classics do not come alive for the reader and the value of the story as a teaching tool is lost. In teaching students literature, it is important to begin with material written in the language of the students, and stories put in settings they understand. Once students are competent in understanding contemporary literature, they are more likely to wish to continue with more difficult material.

"Because literature, and the act of reading it, teaches us more about ourselves, about the human condition, about life, then we could ever learn in school."

As an ex-literature teacher, I am most sympathetic to your objectives. But sentences like the one above feel superficial to me -- for behind what is "taught" must be cultivated a curiosity about the entire human story, an incentive that you won't just be taught (more school stuff) but that the experience is full of pleasure. You make it sound like we should read Hamlet for the Messages, the teaching part, the content, when I think it's mainly about the play of words and action, style and drama-- in short, the entertainment value.

You also skim over the core knowledge necessary to make in-depth sense of remote texts. You can't just start reading even Shakespeare "on your own" unless you have a terrific literary sensibility. I ended up with a Ph.D. in English but reading great drama in high school was drudgery because I couldn't imagine the staging and the sequences. It never came alive just by reading like an innocent.

Frankly, I think if you want to engage classic literature, you should find a good teacher and a committed group of students, wherever that may be (and yes, you could certainly create a Classics Book Club but somebody in it better know something about the periods and the assumptions of authors and writers alike or too much will pass over or under their heads).

In a word, I would begin with the most accessible, and perhaps greatest narrative I know, which is Fagels translation of the Odyssey. Western literature is all there, plus it's the greatest story every told -- about tribe, family, marriage, children, bad manners, making a life, pragmatism (even rank expedience) warriors and honor, and the relationship of man with higher powers, however they emerge.

And I think the chronological model, while logical, doesn't allow for bringing in modern versions of classics, which are closer to the reader today. Excerpts from all the Ulysses lore, in verse or prose, would animate Homer.