Then surely the passengers of a plane wouldn't have problems with pilot and co-pilot leaving the cockpit and getting drunk partying with the flight attendants while the AP is doing it's thing....
There have been quite a lot of movies showing just this sort of thing. Doesn't matter that it's not real, it's what the public see. As they are generally not privy to (and seldom interested in) what happens in the cockpit, they have no indicator to show otherwise.
Hence the common belief that aside from take off and landing (the two most dangerous bits of flight after all) there really is nothing for the crew to do other than a cursory glance at things - or responding to an alarm/radio message should something come up.
I do know that you can cause a plane to turn by setting the AP on and then adjusting a tiny little knob smaller than the volume control on most stereos to set the bearing. If the plane can follow that, then surely it's only a small jump in software to make it be able to follow a number of waypoints? I mean the exceptionally realistic (according to the marketing blurb) "Janes WWII Fighers" showed that 1940s fighter planes could do just that - follow a course of waypoints without the pilot having to do anything. If they could do it back then, why not now? (No, I know that's not realistic - at least I'm pretty sure it's not - the point is the game is supposed to be realistic, I know real planes can be turned by a small knob and a bit of computer power, I also know real planes were having a problem with too much automation (according to other commentards), so really I have no reason to believe (other than other commentards posts) that planes cannot fully fly themselves - as I said earlier I've even sat in the cockpit with the crew chatting with me and seeming to not be paying any attention to the controls or instruments)