Not sure I fully agree. I feel some races have been integrated in human/Stormwind society longer than others. I feel like Dwarves and Gnomes have been living among and working with humans for so long that them holding high offices in Stormwind shouldn’t exactly be a rarity. I could even see the odd Night elf, Draenei or even Pandaren having an important public function though those would probably be much less common.
Then there are the “newer” allies such as the Lightforged (who haven’t had the time to advance through the ranks as much), the Void Elves (who were Horde agents until recently), the Dark Irons (probably more than a bit of bad blood between us and some others in the Alliance).