So far in the game AI cores are for colony management, or dumping into a factions recycling bin (Unless you are Tri-Tach then you just probably hook it up to the Sector's equivalent of the Internet so it can troll Luddic Church nerds).
Unless I'm missing something.
What about the ability to use Gamma, Beta, and even Alpha cores as ship officers? Each core gives you a one time "Generate AI Officer" option that gives you a AI captain but consumes that singular core. And the option lets you randomly generate an AI captain with a set of skills a normal human captain would have, with Gamma having a basic low level captains worth of skill points (I have too many Gamma cores holy crap I just wanna duct tape like dozen of them together to make one alpha core), while an Alpha level is basically a max level captain with bonuses for being the latest version of sentient Windows.
Of course you probably don't need to actually pay the AI captains, and all three levels of AI captains have their own set of bonus that progressively gets better as you go from Gamma core to Alpha cores.
The main incentive to use AI captains is that they allow you to go over the limit of officers you can have, so you can go pass the 10+ officer limit. But a major downside is that if a patrol of a faction that hates AI makes contact with your fleet and searches them there is a huge chance they will find out your fleet has MURDERBOT.exe acting as captain, the faction immediately brands you criminal and starts hunting you down.
Another downside to somewhat balance this is the amount and quality of AI captains you can actually use in your fleet, a bit like the deployment costs for ships in combat. So say you can use a large amount of somewhat stupid Gamma Captains, but can only use say one or two Alpha captains.
Another thing I thought up of if is if you can attack the occasional shipping convoy and find AI cores in them, particularly luddic church, and Tri-Tach convoys. If you take these cores to a Remnant red beacon system, you can give them to the Nexus there and who know maybe you can make some robot friends because you brought back some poor Beta core's girlfriend.