most of the shippy stuff focusses on the relationship, rather than being character studies that happen to have a pairing

Yep, what you said! That's the kind of fic I can get behind - stuff with a plot that just happens to involve a pairing (unless it's really OOC and has Hotch declaring his love for Reid in the middle of the bullpen, because, um, no). Other than that, non-canon ships just don't work that well for me in this fandom. Fics that have Garcia and Morgan being all flirty and snuggly are fine, because that's somewhat canon (and let's face it, they're both really quite tasty).