A big part of the problem here is that we're talking apples and oranges; it's been said upthread. Classics is not a genre, a la SF or romance or mystery, any of which could qualify as a classic. As a big umbrella category, classic isn't terribly limiting in regard to genre (no manga?). The limitation is to restrict it to books which have been time-tested and are highly regarded; they have made it past the stage in which a work is merely dated or of period interest.
From my POV, SFF tends to take over a lot of other categories. I love humor, but the nominee a month ago was SF humor. I passed, but I happily gleaned several suggestions from the nomination list.
We also have more than one "open" category, next month even. if it seems important to mandate a genre not listed (especially if you find that open months tend to be redundant), why not co-opt one of those months to historical fiction, or what have you? Would that "broaden the appeal?"
Finally, while the Literary Book Club may read classics, that's not the point of it. It can be any book which is considered to have literary merit and not just popular appeal. It can be a classic, but it doesn't have to be.
I think the conflation of the terms genre and category has caused a lot of the head-butting here.