I think we can agree though that modern CGBC shows though are definitely inferior and smell of being tugged by too much by marketing influences. They simply lack the grace and elegance older ones do. And the humour.
Different strokes. There can be more than one primordial anything, of course, and Aria came before Minami-ke (both as manga and anime) but in any case I've never considered M-K a CGBC series. Yes, there are cute girls in it - but thematically it's a situation comedy than relies on the humor more than the cuteness. It also has a very strong supporting male cast. To me, it just doesn't fit the definition.
As for Azumanga Daioh, I confess I could never make it through that show. So I guess I can't say one way or the other!