"Airplane autopilots will happily fly into other airplanes"
No. Most (if not all) have ACARS installed. If the plane is going to collide with another plane then between the two planes one climbs above and one dives below. This happens regardless of pilot input.
Unless they both decide to dive or climb at the same time, of course.
As well as that, throughout the flight, a pilot can adjust the speed of the plane and the direction and the autopilot won't disengage. The only time a plane's autopilot disengages is when it encounters something beyond the scope of what it's capable of. For example, conflicting reports from the Captain's and 2nd Officiers altimeters.
At the point of flying in to a mountain, as far as I know, the autopilot will disengage and allow the pilot to regain full control. But regardless, a plane could take off, fly and land with the autopilot on without any input from the pilot. In fact a lot of airlines require a plane to land using autopilot only.
When the autopilot disengages and the pilot doesn't take over the plane DOESN'T crash?
No, didn't think so.