It just seems like software could pretty easily compute non-intersecting flight paths for all planes and assign them accordingly. As well it could real time monitor all trajectories and continue to give out the updated flight paths. I don't see why you also couldn't run a trillion tests using real and simulated flight data to make sure it works well.

Air traffic control has a lot more things to deal with. There are scenarios like runway closed and all traffic has to be diverted. Loss of communication. Various emergencies. Weather changes. It's not just a question of 3D motion planning. Controllers in the tower also use their eyes.

In your imaginary system how is the software "tower" communicating with airplanes, using voice? I don't think we even have software that can reliably decode the variety of human voices over radio that a controller can respond to.

One can imagine a digital protocol to all airplanes but technology works its way really slowly into aviation.

Yes, it would require a piece of hardware, but that seems easy to regulate and wouldn't need to be very expensive certainly not in relation to the costs of owning and operating an airplane.

Seems like you’ve stumbled onto a very obvious solution that would be easy to implement and that no one else has ever managed to see, but which would totally revolutionize the airline industry. Time to start a business!

Because right now airplanes are flown by humans. A large part of atcs jobs is dealing with humans. Not every pilot will be able to fly the optimum flight path.