I think that although there are in-extremis recovery techniques for most sort of LoC scenarios, the very fact that the departure from the normal flight regime has happened while the pilot was on the controls and maybe because they were on the controls, it means that they are unlikely to be able to take much appropriate action in the near future as they have basically lost SA. Near the ground that’s often fatal.
It’s been a while since I was on the 737 but I do remember doing a lot of GAs during sim and base training in various configurations. There were certainly issues with thrust and trim but not unsurmountable ones and after a few goes you got the general idea. The nastiest one was probably a CAT III auto approach with an engine failure on the GA: the aircraft was out-of-trim in all three axes and required some deft handling to get it back on an even keel...