Hmm. Seems to me that the SG doesn't really need a general right now, and what's left of "Azure City" doesn't really need a prime minister so much as a war leader.
Umm. Not entirely. You're thinking of a modern organisation, which is several orders of magnitude larger and more complex than anything that existed in Azure City even before its conquest. If you look at historical generals of even comparatively modern times - Napoleon's day, say - you'll see the good ones did pay enormous attention to detail. Not that they micromanaged every decision, of course, but they certainly expected their orders to be followed, and any officer who 'dragged their feet' as you describe elsewhere could expect to be given a very uncomfortable time.
But 'now' is precisely when Azure City needs a hero for a shepherd. Assuming (best case) the Azurites can regroup, reinvade, and boot Gobbotopia out within the next year, I would still expect there to follow at least 6-8 years of 'emergency' administration (basically, martial law) while the city rebuilds and repopulates. Hinjo just happens to be in charge at a time that gives him a chance to shine - and maybe redeem his catastrophic mishandling of the first Battle for Azure City.