This is also ignoring the fact that soldiers are now suddenly the most undesirable individuals in the world, [...] What is stopping entire detachments from going rogue and merely turning into survivalist strongarms?
Fixed for internal consistency. Army thugs terrorising civilians for their personal benefit are a threat to the species, not an asset, and if you fantasise on becoming such a little armed bully, know that the bullet that kills you will most likely come from behind - from actual soldiers you thought you represented. They weren't taught hutu good, tutsi bad
from their birth, when you find some lone girl, shooting her in the kneecaps, raping her and leaving her to the zombies will NOT make you a hero to them.
Fact is, if the army really does collapses, what most soldiers will do is go home and find their family, not pretend to be several thousands of individual Rambos living out their teenager fantasies. They'll probably grab equipment on the way out, base might not be so plentiful after they leave. As to the ones who do act like little boys' wet dream, in the end... they'll cause immense damage, fight each others as much as the civilian enemy and the zombie annoyance (in that order), and if society comes back on its feet, they'll land in prison and never come out again.
My father was an army thug. It ended in dishonourable discharge. The army does not like army thugs. It tolerates them to a point as cannon fodder can come in handy, but there's a level of unwarranted sense of entitlement that becomes a liability to any organisation.
P.S.: Chain of command and chain of supplies run parallel. You no longer receive orders and think you're now the king of the hill? You no longer receive ammunition or food either! And organisation does mean that in a combat situation, the soldiers know their job well enough not to need ridiculous micromanagement; if you think that means you could dump them in a situation without a common objective and expect the same result, you should watch less TV.