|Skeptical reader is skeptical.|
This kind of thinking will send a reader 'round the bend.
The question of what makes a book worthwhile to be one of the 3,000 is highly subjective—though scholars might argue otherwise. The last chapter of Terry Eagleton's How to Read Literature, "Value," contains the author's argument of the futility of trying to classify some books as the "best." Eagleton sets up and knocks down all of these criteria: originality, language, technical skill, asking big questions. The truth is that books go in and out of fashion. Ask a dozen people and you'll get a dozen answers about what a reader should read in their lifetime.
Trying to choose the 3,000 "best" books will not only drive a reader out of their minds. It will also, slowly but inexorably, suck the joy out of reading. Joyce, Proust, Melville, Woolf, and Faulkner are perennial entries on lists of best books. They are not on my lists. I know enough about myself as a reading to know that I would have to force my way through them. I don't know if I'd last a chapter before I was longing to read something else, anything else, even my shampoo bottle, than another chapter of Joyce or Proust. Some readers may adore these writers; I know they're not for me.
I suspect that I'll spend my last reading days reading (or re-reading) books that are pure fun.