When things go fine, they're essentially working at a button factory. The situations where they aren't are when things go bad.
In general, space traffic controllers would do a few things:
1. Confirm someone's intending to land at the station, and verify peaceful intent on approach.
2. Figure out which docking bay is free for that given ship to use, and indicate to the ship where it is, and provide a note to other air traffic controllers that said dock is being used.
3. Confirm that ships leaving a docking area have clearance to leave/aren't on lockdown, and that the area is clear for them to leave.
4. Keep track of when ships leave a dock and that dock opens up for another ship, and pass that information to other air traffic controllers so that they know that dock is now freed up.
5. Confirm that the ships know where they're going, and that they are, in fact, going there. 500
And that they can, in fact, get there.
5.) is where things become complicated; because things can go wrong on any of the other steps. Because most of the time, when you give a person a dock, they can get to that dock, or request a closer one. But emergencies, you run into issues of where they can dock in an emergency.
If, say, a stray micrometeorite destroys their engines, you might end up in a situation where they need to land, but specifically, can't land back at the dock they just left a few minutes ago because of their current momentum. If your lucky, you can find them another dock in short time - if you're unlucky, you get to prepare emergency recovery services for when they are "Going to be in the Hudson".
Which sort of gets to the core of why you wouldn't dedicate an A.I. to take on the initial steps of this - the Hudson River is not a runway, landing strip, or airplane docking port; your A.I. that tries to handle this is going to have an issue about this and be "particular about it and make it a runway/dock.".
These are rather stressful situations presumably, which is why it's great that those situations are usually rare, and the job is usually a button factory workplace job. You go into work everyday hoping that's the type of day it is; but you never know when it's going to be a "Hudson" day, so the docking station prepares for the case where it is, in fact, one of those days. 500