Personally, I believe English Teachers of the American Variety to be a curse upon the Earth except for a few. (Mrs. Nelson, you were one of the good ones. God took you too soon.) Regardless, they have mostly forced the dredges of literature on the American children for far too long. The "Red Badge of Courage"! Baa! A short story to detail the use of color as a metaphor. If it was Shakespeare , the cackling conspiracy forced that dreadful play about those two idiot teenagers in Verona who murdered each other for a brief fling until I was Sophomore in High School. That is probably why I love "Julius Caesar" so much because it wasn't that dreadful play about teenagers.
That and I got to be Julius Caesar as we acted it out.
Regardless if I had my way, there would be removal of dreadful pieces of literature from requirements such as anything by Thomas Hardy. Also, Thomas Hardy should just be forgotten by humanity in general. Dickens would be toned down except for Tale of Two Cities and A Christmas Carol which I like. There would be more Arthurian literature in there with the Once and Future King and possibly some excerpt of Le Morte D'Arthur for comparison. And by the grace of God, his son, and all of the choirs of angels, the science-fiction part of any literature course will not have "Dark They Were, and Golden-Eyed" by Ray Bradbury. That story still freaks me out. There are better Ray Bradbury stories by a thousandfold than that one, and I'd rather be something that inspires the children's dreams instead of their nightmares.
As for classics, I'd argue that if they had an impact on the culture they get the title. Gatsby did, but I'd argue other than giving us the name of the Princess Zelda in the Legend of Zelda series, the impact has been for the worse than the better. The characters are awful people, and nothing is really wasted in life if you don't read the book.