To get the sort of posts that appear in the off-topic sections of forums, I think there'd have to be a specifically off-topic section, in addition to miscellaneous-but-relevant. It feels like there's some pressure in this community (though it might be only my perception - I don't think anyone is trying to pressure people) to keep posts to a high standard, so we'd need to explicitly make a place where it's okay to talk about cat videos and minor life events and the weather if we wanted to be able to talk about that. (Though there are probably other ways of indicating that it's okay to go off topic - after getting it started, having off-topic threads that don't get downvoted might be enough.)

I would prefer not to have an off-topic subreddit. I fear that it would attract the sort of people who aren't as interested in the core topics here and ultimately dilute the quality of the community.

Reddit /r/lesswrong exists.