Teachers and Administrators are equally as committed to 'keeping their jobs'.
It just so happens that 'teaching' is mostly 'teaching' and all you can do is 'teach' and so long as you have kids in front of you 'it's working'.
The scope of their roles doesn't allow for them to go too far away from 'the mission'.
Administrators are not default committed to the 'org' they're just in a position where their decisions and actions may or may not further the mission.
'Very Bad Teaching' is rare and usually self evident. With administration, it's not so clear.
NASA Engineers are not like teachers, in that, the could be wasting a lot of time and energy. Maybe the risk is worth it in some cases (?) in others, maybe not so much.
FYI - in teaching, the biggest costs are generally the 'teachers'. etc..
Regular Public Schools aren't a good opportunity so much to demonstrate this 'Law'.
A not-quite-independent entity like a Post Office might be. They often fight directly against innovation due to the risk it may create to jobs for rank and file, and don't quite have the same competitive basis as others.
I know it's difficult to understand, but organizing people around large and complex goals is hard, and I wouldn't say that it requires a 'submission of autonomy' ... but it does mean that people's roles become much more narrow and that it's really hard to see every move in the big picture.
The best place to see it is in the military, where people are often thrown in situations with much higher risk etc. where the payoff might not be as much as we'd like ... but if we want to defeat Hitler, that's pretty much the way it's going to be. Soldiers in 'good armies' get to make decisions about the tactical bound in front of them and not much beyond that. No 'big picture' stuff.
Most of corporate America is highly inefficient but it's also not that bad.
Another way to understand it is that inefficiency means underutilization ... but we still show up and have meetings to fill time anyhow. Like some managers could work 25% of the time and do just as well, but their jobs are mostly still important.
It's hard to see that often from a 'single position' - how doing XYZ might seem perfectly obviously in the companies best interest but it may not be able to work that way. Though of course often it is.
First, there will be those who are devoted to the goals of the organization. Examples are dedicated classroom teachers in an educational bureaucracy, many of the engineers and launch technicians and scientists at NASA, even some agricultural scientists and advisors in the former Soviet Union collective farming administration.
Secondly, there will be those dedicated to the organization itself. Examples are many of the administrators in the education system, many professors of education, many teachers union officials, much of the NASA headquarters staff, etc.
The Iron Law states that in every case the second group will gain and keep control of the organization. It will write the rules, and control promotions within the organization.”
— https://www.jerrypournelle.com/reports/jerryp/iron.html