Of course it can be done, and unlike the dog walking on its hind legs, it can be done well. Given the level of automation available in modern aircraft, it's much easier to do a self-flying airliner than a self-driving car, because the environment is so much more controlled.
To me the puzzle is why Airbus are spending so much money on this.
Scenario 1: fully autonomous — nobody in the cockpit (maybe no cockpit). Remember the old joke about the automatic announcement saying "Nothing can go wrong ... go wrong ... go wrong ..."? However cheap the tickets were, I don't think it'd survive the first crash – and there would be a crash, because the world is imperfect and AI isn't really that clever. Murphy's law says something unexpected would be certain to happen that the automation couldn't cope with. Then parabellum's point about liability kicks in.
Scenario 2: supervised autonomous — pilot lines up for takeoff, presses a button and goes to sleep until the aircraft either lands or wakes him/her up because something odd is happening. Just feasible, but puts back most of the cost because you've got to have a fully-functioning cockpit with at least one competent pilot in it.