There's a double meaning to "wants to have read." I've always thought that Twain meant "wants to be read by others" or "wants others to read." That is, a classic is a book about which everyone says, hypocritically, you should read this book, but I don't want to read it. To me, it doesn't mean you should read this book aloud to me, just that you should suffer the boredom and puzzlement involved in reading it, because it's "great literature" that someone should read, but I don't want to go through that hassle myself.
I had not thought until I read this thread that Twain meant by "wants to have read" that people want to be able to say after finishing it that they have read it themselves, but don't actually want to go through the process of reading it. But tht's also a reasonable interpretation of "wants to have read."