Well, the only automated system we have is cyclops, which isn't so great. It tends to beep sometimes when it shouldn't.
The system where the players make the challenge is based on video footage. And I guess it since it takes a bit of time to make up the picture that shows the flight of the ball (hence the breaks while waiting for hawk-eye calls) an automatic system would be very time consuming. If no one complains, then out calls would be made after the ball actually misses, while the players are still rallying, and it'd be inconvenient.
Not to mention it completely removes the human element. Linespeople and umpires would be completely removed.
Research Lab - The physics is theoretical but the fun is real