Uneducated guesses:
My impression is that it's at least partially down to how brittle a fully automated system could be. You want as much of a "manual" backup as possible, and that only be achieved by doing things manually all the time to keep up practice. With the current system, even with enormous degradation (massive power outages, cyberattack, software flaw, etc.) it's possible to get planes out of the sky without much risk. If a fully automated system fails, it's an enormous disaster.
The other problem is that the "worse is better" arrangement where ~everything is done via voice over radio makes automation difficult. Voice is simple, universal, and enormously flexible, but hard for computers to handle systematically. Some two-way protocol and associated pilot UI would be useful... but then you have to decide on that protocol and UI, every manufacturer has to implement it, every airline has to buy it, and every pilot has to be trained. Unless it's very, very clear what the optimal solution is and that the benefit outweighs the cost, that sort of coordination is difficult.
(And remember, the ultimate result of such a change would be a rigid system that is difficult to change, more fragile, and does not save much money relative to the total cost of the airline industry.)