Agree. My (one and only) experience with using Stack Overflow for Facebook questions was not especially positive, and after having my motives impugned and my question derided as purposeless I just deleted it. (No point arguing with the police.) Sadly this was not the first time I'd had this experience on SO, even if it was my first time using it as any kind of official-looking support channel, and I would therefore look askance at any organisation using SO proper for their support.
On the other hand, I've noticed a couple of companies using their own Stack Overflow install for their support forums, and I'm sure that could work pretty well. It's not a question of the software, just whether or not the community is right, really. SO's has ended up with too many volunteer bureaucrats, I think, and to make things worse there's even a meta site where they can gather and make up more rules for people to follow. You say organised, I say ossified... well, let's call the whole thing off. I stopped posting on SO after my last experience.
I don't expect anybody to care about one person leaving (and nor should they!) but if enough individual people leave, then I guess eventually nobody will be left.