@Centaurus it becomes even more weird when you have experienced that the 737 can quite wonderfully use the autothrust in OEI flight as well as keep the rudder where it belongs as well, thus providing full automatic flight.
Is an autopilot rudder channel available on B737? None I've flown. Every QRH I've seen B733/737/738 has instructed A/T off with SE ops. True, if an engine fails in CRZ the A/T will increase and try to maintain speed. I'm not sure how long it will remain connected. On takeoff it will disconnect during climb out.
Question to the AB pilots: when flying an approach with A/T engaged do you follow through on the T/L's? If not where do you have your inside hand? I suspect the B777 Asiana PF had both hands on the yoke; might be wrong.