Do you think it's wrong to say that "great literature" (by which I mean things like Shakespeare or The Great Gatsby) is read mainly to signal intelligence/culturedness? I really think it is, because for instance it impresses people, and it's difficult, and it's not as fun as most things you could read, and I don't think reading (a small amount of) "great literature" has taught me anything useful for anything other than signalling. By saying I think it's about signalling I'm not trying to imply that it's wrong or that you shouldn't do it, but if you know you're signalling then you can optimize for signalling (by e.g. reading summaries rather than the original).

I've read a lot of "great literature", and I will admit that signalling is a big motivation. Many of my friends are academics in the humanities and I'm often involved in conversations where references to Dostoevsky, Henry James, etc. are frequent (again, probably to signal intelligence and culture). Not being familiar with literature would incur a significant social cost in that context.

That said, I do also legitimately enjoy much great literature. Not so much because I learn a lot from it (although I wouldn't say I don't), but because a lot of it is actually brilliantly written and involves deep and interesting ideas. As a contrast, I also have friends who are really into anime, and they often talk about it. I've tried getting into it, but I've found even the most acclaimed animes (Cowboy Bebop and Death Note are ones I've tried watching) to be dull and somewhat silly. I just can't get into the aesthetic. I pay a social cost for this -- I often feel left out of the conversation when I'm hanging out with my anime-loving friends -- but that isn't enough to force me to watch these series.

So signalling is definitely a big part of why I read literature, but it's not a sufficient reason. If I didn't enjoy it I doubt I would force myself to do it.