On Proper Nouns

My son is learning about proper nouns and common nouns at school. Which led to my griping last night about that particular dichotomy in English. Iraq is a proper noun. That makes sense. Iraqis is as well. That doesn’t — there are millions of them, if that doesn’t define “common” then I don’t know what does. To the argument that being an Iraqi is an matter of identity, I counter that if that’s true, then words like Muslim should be considered proper nouns as well, but they aren’t. None of this would matter that much if I wasn’t staring at IRAQIS in a recent Scrabble game, unable to use that awesome triple-word layout just staring at me.