Writers as book club members: Is it even possible?

When we first moved to rural Pennsylvania three years ago, a few well-meaning folks suggested I join a book club to get to know like-minded people.
I thought about it ... for about two minutes.
While I would greatly enjoy the wine (What's a book club without wine?) and the socialization, I know I would be a lousy and annoying member.
I cannot think of a novel I have read in at least the past two decades without an edge of criticism, and it's not the kind of criticism other readers would want to hear.
It's sentence structure.
It's word choices.
It's how well and with how much artistry the author has suspended my disbelief.
It's logical flow of plot and voice.
It's pacing.
It's whether the facts are right (because, yes, a good author strives for accuracy even in fiction).
While other members reach for deeper meaning, I can imagine myself reaching for a red pen.
So my question is this: Am alone in this?
Can writers succeed as book club members?
Or should we just skip the criticism and stick with the wine?
Do you, as a writer belong to a book club, or do your book club have a writer as a member?