Why is air traffic control done manually by humans?
Having it explained to me briefly what exactly the tower does that cannot be handled by such a system would probably enlighten me somewhat.


Fair warning, that's my job you're trying to replace with a computer, so I'm probably biased. Still though, hear me out:

What do we do?


Handle a large amount of non-standard requests and communication between the cockpit, the airport, the airlines, flight schools, fire and rescue, authorities and many other parties
Deal with vehicles or even individual persons moving on the maneuvering area, where the only available communication is an (analogue) handheld radio
Identify obstructions or animals (such as birds) on and around the airport
Deal with smaller general aviation aircraft with no sort of digital communication, only a radio. Sport aircraft, gliders, hot air balloons.
Deal with individual aircraft without transponder (not visible on radar). A digital system would have no way of knowing where the aircraft are.
Handle traffic at entire airports without radar coverage. A digital system would have no way of knowing where any aircraft are.
Deal with aircraft with no flightplan (only way to know what the pilot wants is to talk on the radio)
Make decisions not only based on what is said, but also how it is said. It's quite easy to notice an inexperienced trainee pilot on the radio, and they need a bit more space and might not always do what they're told
Setting the runway lights to an appropriate level based on a number of factors (darkness, visibility), some of which are not easily measured digitally
See, visibly, when an aircraft enters or leaves the runway (most airports don't have ground surveillance, so the only way to determine the position of aircraft is to look out the window)


Could these things be solved/handled by a computer? In theory, sure. You could:


Invent some sort of artificial intelligence that intuitively knows exactly what someone means as they say it, and know who to forward the message to.
Replace all aircraft vehicles worldwide with fully autonomous, self-driving Teslas that can communicate with a central control system.
Install a number of high definition cameras on every airport worldwide, and use artificial intelligence to classify visible objects. Then alert the self-driving Teslas to go and scare the birds away.
Force millions of hobby pilots and flight schools worldwide to invest thousands of dollars in new equipment that can communicate with a new digital ATC system (before that: actually invent that equipment, and get it certified worldwide)
Force millions of hobby pilots and flights schools worldwide to invest thousands of dollars in transponders. Invent new light-weight batteries that enable the installation of transponders in light weight aircraft, gliders and hot air balloons.
Install thousands of new radar stations worldwide. Invent a way to deal with garbling and FRUIT caused by all the new radars.
Force all pilots to file a flightplan prior to flying. Change the flightplan format so that it is much more accurate than it is today, and teach all pilots worldwide the new format. Force all small, single-engine planes to always be flown by two pilots: one will fly the plane, the other will be busy on the iPad, changing the flightplan in real time as the flight progresses, since a short message over the radio is not an option (a digital system wouldn't understand it)
Assume the worst case scenario for all flights. Add extra separation between all aircraft. Reduce capacity at many airports by 50%, thus increasing delay by millions of hours worldwide.
Install a light control panel in the cockpit of every aircraft in the world. Teach all the pilots to use it, install redundancy systems in case it fails.
Since we've already made everyone buy transponders, why not install ground radar in every airport in the world? Will probably only cost a few million dollars per airport.


Last but not least, invent the system that actually processes all this data, to replace the decision making that is today done by air traffic controllers. Have it work in every single edge case, in every airport, in every type of climate and weather conditions, with every aircraft type, with every type of flight - and have it certified by aviation authorities worldwide.

Anyway, I think you see where I'm going with this. Is training air traffic controllers expensive? Yes. Do humans make mistakes? Yes. Would creating and getting certified a new digital system be cheaper? Absolutely not. Would it be safer? In the long term, maybe marginally. In the short term - most likely the opposite.