These days it would be impressive if all high school seniors could even read.
As to the question, I am a big fan of quality over quantity. I took one class in college where we spent half the semester on a single book and it was a great experience. With that much time you can actually read the book in depth, think about it and then have profound discussions. I never thought high school made sense where they try and cram as many books through as possible. The result of that I think is that kids just end up frustrated. So, I think it would be better to focus on the process--in depth reading, critical thinking, and discussion--rather than worrying too much about the specific content. Any great classic will do.