The use of Dual A/P has lead many into problems if disconnected with back trim and not dealt with promptly.
Flew that a few days ago in the real world. Saw the lights 20 feet above minimum, disconnected and landed without a hitch. Could have let the automatics do it as well, but without protected areas in marginal weather that is not a bright idea. Flying the 737 with back trim in is a non-event for any halfway competent pilot. Keep a bit of forward pressure in while you trim off the back trim and land or go around. Yes, in a go around there is additional pitch up because of the pretty strong pitch power couple in the 737, but then again that is nothing new or challenging.
Letting the plane fly itself without autopilot is a bad idea, and was a bad idea even in that very first puddlejumper we all flew at some point.