I think you have just described what happened with the Asiana 777!
Errr no, on the 777 if you hit the TOGA switches (in the same place as the 737NG) with the auto throttle arm switches in the arm position (normal) you will get GA thrust.....of course an aviator will have one hand on the thrust levers and one the yoke..just in case
The FD will pop up and give you GA guidance, but will disappear again when you select another mode....which is why...regardless of SOP's I always ensure I have my FD back on by 300 AGL on a visual approach...as it's going to help me not f@@k up the ensuing low level GA that will invariably be required when I least expect it whilst hand flying.