I don't recognise this from the Culture novels. Plenty of Bad Stuff happens to people (and all manner of beings, drones, Minds, etc.), but that generally does happen in fiction. I can only think of one Culture novel that kind of has a "revenge plot" (Surface Detail, and it's probably not the main theme of the novel).
> it's like he couldn't quite come up with much to write about that was within the Culture per se
I think it's possible that Banks thought writing purely about a utopia would be boring. Personally I would have read anything Banks wrote in the setting, even if it was just a story about everyday life.
If you haven't read it, his text (short story? Fictional article?) "A Few Notes On The Culture" is quite interesting and devoid of Bad Things Happening: http://www.vavatch.co.uk/books/banks/cultnote.htm