Seems like I'm quite late to the party, but I'd like to pitch in my two cents since I have some experience playing IAA.
As pretty much everyone has said, IAA as a role is having an identity crisis. Magistrates(although I have very seldom seen the Magistrate doing anything more than deciding how to punish perma prisoners), representing the Security and Legal Departments, seem to enjoy having control over IAAs, even though in my experience very little has actually come from this relationship, the IAA perhaps being asked to corroborate a report or serve as a placeholder until the Magistrate is avaliable, but no actual "legal" activity, per se. At the very best, the IAA is designated to deal with events deemed to minor for Security to handle(and knowing Security, that's an incredibly small number of incidents)and the Magistrate is busy. The idea of a civilian authority over Security too, seems great, but from my experience, IAAs are ignored, occasionally even actively disregarded, by the whole department, the Detective being the notable exception as they can relate in being in a somewhat sidelined, and very situational position.
On the other hand, though I do not often directly interact with the NT Rep, my play-style(and that of the majority of others that I've observed)follows very closely to the HR Complaints/SOP Investigations that the NT Rep is assigned to facilitate. Anything from paperwork to SOP check-ups seem to me more of a fit for the role, essentially the resident bureaucrat rather than some random arbiter. To me, conducting small-scale check-ups on the different departments is much more beneficial than being involved in legal affairs, as it could prevent an entire Security Team having to be sent down to Mining, or the like. The middle ground that is investigating Security would, rather than half-hearted suggestions over the Security Comms, take the form of a fax to CC, or a meaningful complaint to the HoP, Captain or NT Rep(though any sort of CC intervention would probably get redundant, given how often the Security team takes liberties in their position).
In my opinion, doing away with IA's obligations to the Security Department would be optimal. They'd still be on the same Comms, and would investigate Security as they would any other department, but all the(ill-defined)baggage that comes with being pushed into the very non-existent legal scene would no longer prevent the IAA from pro-actively conducting investigations out of fear that they might be called up to deal with some legal issue. Going a step further, for IAAs to have a greater impact on the round, ensuring SOP is being followed, I'd encourage they be given some(obviously non-violent)leverage over the Security Department, as it's quite, quite impossible for the IAA(and pretty much any other civilian force on the station)to regulate the officers when they have power in the form of weapons. At the very least, those who play IAA have to break through the mentality of being part of the Security Department, as Security is just as, if not more, liable to SOP violations when compared to other departments.