Now, consider that programmers make mistakes (even in aerospace) much more frequently than pilots decide to commit suicide. If a software system is given first-authority instead of a pilot you'll have more deaths due to the system than due to pilots intentional attempt to destroy a plane. The problem of suicidal pilots can be addressed by a number of known mechanisms, none of which jeopardize the safety of a flight. Pernicious problems of software quality are still incredibly difficult to address in any context.
As to "why is it not implemented" - because it would create far, far more problems than it would solve, without a measurable benefit.
All the technology exists for me to build a drone swarm to patrol my house constantly on the inside and out, deliver me a video stream, and to deter intruders with non-lethal force. That doesn't mean I just need to order the parts, assemble them, and use.
There is no off the shelf remote fly-by-wire for an Airbus A320 or any other passenger jet. Plenty of companies have done it as a one-off thing. This is for either testing UAV systems or using the plane as a crash test vehicle. This usually involves the same team of engineers that equipped the aircraft monitoring every single parameter in real time. The military has actually received criticism for conducting weapon systems 'tests' in this manner.
There is a huge difference between that and commercial operations of such a system. In a commercial environment, you can't have a team of engineers on constant standby. For planes flying for research purposes over unoccupied areas a high risk of total loss of control is completely acceptable. Commercial and military remote control aircraft all have systems that intentionally crash the vehicle if communications is lost and it leaves a designated area. This prevents potential loss of life due to mundane software bugs. You can't ethically build a system that intentionally crashes an airliner full of people as a response to a software bug.
But fuck that co-pilot.
But a pilot with time alone in the cockpit can most likely trick the flight computers into whatever mode he wishes.
In any case, you're right that the automation (by whatever name) can already override the pilot in many cases. But it's a really tricky problem because you can easily make things worse instead of better. For example, one reason that Air France 447 crashed was that one of the pilots was commanding the airplane as if it were in a fly-by-wire mode it was not actually in. The plane had already stalled, but he was flying it as if the computers would prevent him from stalling, rather than taking proper corrective action. A proper recovery maneuver would have saved it. This is ultimately pilot error, but automation is a strong contributing factor. For another example, Asiana 214 crashed because the pilot assumed the airplane was doing more for him than it really was, trusting the automation to keep his speed steady, which it wasn't set to do. Again, pilot error, but with automation as a contributing factor.
It seems likely that automation is a net gain when done right, but it requires careful consideration.
The co-pilot flies. That's why there is a co-pilot.
(On really long flights there can be two co-pilots so that pilots can work in shifts, but medium-range flights like this can physically be flown by one pilot, two are there for safety).