The Instructor job could be, to an extent, covered by IAAs. The problems are, however, self-evident.
Many new officers seem to understand just one thing: IAAs have no authority. They will sometimes even try to disregard Magistrates, incapable of telling the difference.
Many IAAs seem to not understand one thing: Their own SOP.
These lead to more fighting than cooperation.
If a new officer makes a mistake, the most likely reaction from their department is an IAA attacking them. It is a natural reaction to defend yourself, even if you are in the wrong. From there on, things can only escalate.
IAAs have often diplomatic skills of a jellyfish, so yelling and waving around SOP books is their default response where one can much more efficiently "ensure that Standard Operating Procedure is being properly followed" by proving it's beneficial to the officer. If they can't provide a reasoning to support something, why the officer should listen to you?
Why Instructor, in whatever form implemented, could positively affect this situation?
As a senior officer, he will be immediately more respected. Now, yes, there will be cases of people not respecting them, but they are the same people who die 10 minutes into round somewhere in the maintenance. They are hopeless and Instructor isn't there to bother with them, maybe just to root them out.
Officers who have the right mindset will be facing a less impartial teacher. Someone who will, ideally, tell that pedantic IAA to fuck off, they've got it covered. Sure, this will piss IAAs even more, but majority of them is perpetually angry anyway.
That is obviously just the part where IA and Security actually interact - the Brig. It's quite clear the Instructor's responsibilities would extend far out of it and to much greater extent. You could say it would be fooling around and wasting Security's resources, but if the Instructor was willing to, they could easily train new officers in combat in rather safe environment. It's not like they will go blind if they take SEChud off and let their pupil see how flashes work. Bolas won't gib them. And if they decide to practice melee... well, I don't actually expect them to let someone harmbaton them to see how bad it is.
Outside of the brig, they could provide valuable insight and much needed backup in case things go terribly wrong. Learning security with someone watching your back might lead to a certain dependency, but I think depending on other officers is the key to success in Security. You can't be everywhere. You can't do everything alone. So why not make pairing up the first thing you learn in Security?
Regarding Cadets, this seems a bit redundant. To make this job relevant, you would have to either put a significant playtime gate on regular officers (suggested 2-4 hours above seem too little) or make their equipment much worse. While the former might be accepted, the latter would directly disrupt the Instructor's job, as the people they are teaching won't have access to the necessary tools.