I would argue it's the inverse - Fate treats combat the way it treats everything else.
I believe that's Diaspora (based on Fate). That's not how most Fate games deal with social encounters.
It *is* the big roleplaying game, regardless of its suitability for the task (which I am not placing any statement on, one way or the other).
As far as the OP goes - cut the wargame roots if you want to. Others won't if they don't want to.