It's easy to look at the second key principle of Bastion (Nobody know who's in charge) in isolation and imagine an anarchic city without any sort of government.
But instead look at all three together when you're trying to think about how the city works.
1. Everything is Here (including a government, police force, military, judiciary system, and most other civil services you can imagine. Bastion draws in the biggest movers and shakers, so you can bet they're trying to move and shake things).
2. Nobody Knows Who's in Charge (for every piece of government, there's somebody else claiming to be the legitimate version, and another group on the far side of the city, and another in the Underground).
3. Everything is Complicated (These groups sometimes cooperate, sometimes recognize eachother's legitimacy, sometimes have full on street wars. Getting something written on a piece of paper by one organisation could mean everything, or nothing, to another).
So when you need to bring Bastion's Army out in your game, you get whichever General (often self-appointed) has managed to bring the majority of the city's soldiers together (often in vastly different uniforms) without infighting (usually by suitably looking and acting the part).
Then maybe another general (this one promising more pay than the other) showing up with another Battalion. Maybe they argue, maybe they ignore each other, or maybe a Grand Gold-Star Master-General shows up with his elite cavalry and pulls rank on both of them, pulling them together.
If they recognise his rank.
And if his hat is impressive enough.
If in doubt, stick to those three principle like glue, and remember how to put them into action when creating bits of government in Bastion.
1. Everything is here - Create an interesting Civic Faction that the players will want/need to interact with.
2. Nobody knows who's in charge - Create uncertainty about the legitimacy of the Faction with rivals, or just make them terrible.
3. Everything is complicated - Give the Thing its own ambitions and conflicts.
Follow these and the army example can apply to courts, banks, prisons, post offices, schools, hospitals, and universities.