To play devil's advocate a bit, I would agree that it doesn't fit our main focus as a forum, but I think it's worth noting our focus has changed in the past few years since the site was released. If you were to go back a few years when things were just starting here and tell us that we would have a CAP forum (especially with stuff like AA's modserver at the time) I think we'd probably tell you that you're crazy, but not only do we have it now, but it is (evidently) important enough that contributing to it is basically equivalent to making/editing on-site analyses. Even how those analyses are written might be a decent point of comparison, they're written in a way much more conducive to educating and luring in players new to the competitive scene rather than being written more toward players who are already advanced as they were at the site's inception. Whether we've intended to do so or not, the site's focus has definitely changed the past few years to accommodate a wider variety of users.
I do think, though, it'd be a mistake to hit the anime or the TCG as hard as we do competitive pokemon(and competitive sort of pokemon) because then it definitely would be a questionable dilution of focus, but I imagine an off-topic pokemon would fall under socialization - it's just discussion of a common interest, after all, rather than something that would be an actual Pokemon subforum. I'm not sure how much use we'd get out of it, but I know a lot of people play the TCG still, and I know on IRC at least there's still pretty frequent reminiscing about the old anime episodes...
I think it's something that would be needed to be moderated carefully since we would want to make sure it didn't devolve into some of the community we strove to distance ourselves from with Smogon, but I think if it's done well it could be a fun stress free Pokemon environment... even non-competitive games I know people play like Rumble and Ranger(oh GOD) and the Mystery Dungeons would better go to a forum like that. Since, like I said, it's probably best as a Socialization subforum I'd definitely be willing to moderate it if we change our minds.
It's not like it's going to attract throngs of non-competitive players, as I think the underlying worry is? since we'd have absolutely zero competitive advantage over somewhere like Serebii, which already does the general Pokemon thing about as well as it can be done. It'd simply be somewhere for the users we already have to discuss the other side of Pokemon without having to get their feet wet somewhere like that, which doesn't seem too problematic to me.