I agree wholeheartedly and make it a point to explain through story just such things. I'm actually almost surprised people wouldn't think to do that on their own, at which point I realize what I'm saying and am then surprised I could be surprised at such a thing.

It only takes a little thought to work everything in, then a little editing to shorten it enough that someone would want to read it. If you like your character concept, the editing will be harder than the writing because you won't want to take things away. I've had roles that included both story posts and note posts done for the Imms benefit. I like to think I can be creative without being overly verbose, but it's hard not to fluff.

The Immortals have an easier time interacting with you when you give them everything they need to appear omniscient. Maybe people get confused and think they really are?