Imagine a model:
Everytime a unit is stood up it has a 50/50 chance of having an above average or below average organisational culture. Once stood up, its culture may change over time but only randomly so - 50/50 chance to improve or worsen in a period.
Now how could a(n armed) bureaucracy systematically pursue good organisational culture and thus high performance under such conditions?
The answer is simple, but it goes largely against a bureaucracy's instincts and preferences:
Disband bad units or at least exchange their management and lower-ranking employees (NCOs and enlisted personnel in case of the military).
This is actually done in some extreme cases that became unbearable, such as a couple years ago with the German Wachbataillon (the supersized battalion that protects the ministry of defence etc.). It was known in all of the Bundeswehr as drunkards' central and disciplinary action hot spot for decades until all the water in the tank was exchanged. It happened in the last years of conscription, and they added only conscripts with Abitur (highest school degree) after kicking out all previous enlisted personnel to solve the persistent and embarrassing problem.
There is a huge difference between doing this in the most extreme cases only and doing it regularly as a standard scheme of personnel management.
A certain rule of thumb surfaced in the context of police shootings in the USA; a few per cent (IIRC ~ 15%) of policemen are bad apples that do bad things until kicked out, a few percent are good cops that won't do bad things in any case and the rest turns into more or less bad cops if the organisational culture tolerates bad behaviour. The key difference between trouble law enforcement departments was thus the behaviour of leadership; do they sanction bad behaviour or not, do they kick out bad apples or not?
It's very hard to reverse a bad organisational culture, but the tainted apples moved to a new unit may prove unproblematic if the leadership there doesn't fail. The corrupted department may meanwhile be reset to a good organisational culture with new personnel.
Back to the model. We can add as a rule that the worst 10-30% of units would have their personnel exchanged entirely every year, with some bad apples even kicked out of the service entirely. This would insert a bias towards improvement of organisational culture average over time, and this doesn't even include the incentive effect. Officers would understand that having led one of the units that were found sop bad that full exchange was necessary would be embarrassed* and see their careers badly hurt if not ended. They would be additionally motivated to not tolerate bad behaviour.
Meanwhile, after a while the (armed) bureaucracy as a whole would take pride in its good culture rather than perceive the common personnel exchanges as embarrassments. The bureaucratic resistance to the policy would wither away.
*: I believe in humiliation of bureaucracies as a tool of oversight and disciplinary action against their pursuit of self-interest..