Certainly was picturing it in the fluff section of the page.Perhaps. But probably still in the fluff section. Actually what I feel the stat block should have, is just some brief summary of the combat tactics of the creature (4e had roles, like that but perhaps a bit longer) that helps the GM to properly use the creature in combat ('Ranged skirmisher,' "melee bruiser' etc.) Because that's what you mostly use the stats for. For out of-combat stuff you need to read the fluff section and/or come up with your own fluff. There really is no shortcut for that and I think it is a bad idea to pretend that there could be.
I guess that's how I feel about random tables for things like PCs TBIF's for character creation where I want them to put a lot more thought in. For helping differentiate a group of mooks that would last a scene it didn't feel as bad.