TCAS is much simpler than your proposal. Ensuring that traffic can't get too close to you in midair is a different problem from analyzing complex, non-linear movements at tightly-packed airports. How do you implement this system while avoiding false positives?
Imagine that you're landing at one of two parallel runways. There's a plane lining up on the other runway. You can't have proximity warnings like TCAS, because this is a safe situation even though you get close to the other plane. What if that plane is taxiing towards your runway? You can't predict its movements until it starts entering the runway because it may just stop at the hold short line, as it should. Extrapolate this simple scenario to anything that could ever happen at airports with a large variety of actors, and you'll start to see why everyone in the world is still relying on humans to do this.
