There are only a set number of conversations ATC has with an aircraft so it shouldn't be too hard to implement.
In order from departing a stand to arriving at a stand it's: Route clearance, pushback (if required) and engine start clearance, taxi clearance, takeoff clearance, hand-off, landing clearance, taxi clearance.
Technologies to reduce controller workload could also be included such as following the greens during LVPs to improve efficiency at the airport, supported by the visual effect of the green lights doing the pathfinding. https://www.youtube.com/watch?v=2W2ak94xTXM
However I don't think it should be a heavily worked on feature given that as an office worker (Which is what the manager essentially is) you may (but probably wouldn't) hear the airport announcements, you almost certainly wouldn't hear the ATC chatter, though you may hear jet/prop/vehicle engines and such.
I think it would be much more immersive to have the airport sounds being done really well, proper engine sounds on take-off run and such, rather than the normal woosh with slight whistle you get in most games involving aircraft which sounds really pathetic.
However inside the terminal I definitely think that the announcements should be there as background noise to the game.