I would enjoy being a member of this type of club. Of course, there are loads of differing opinions of what constitutes "literature" but we are talking about what sun surfer calls a "well-regarded work". This still leaves a wide area for exploration. I enjoy the "standard classics" {Jane Austen is my favourite novelist} but I would feel that science-fiction includes a great many very well written works {those by Damon Knight for instance} that could lead to fruitful and interesting discussions. The same would be true of Fantasy.
The means of choosing a book might pose some problems but those of you who have been in clubs of this nature would undoubtedly know how to obviate that. Anyhow, I would like to give it a try!