Following an engine failure after take off in the 737 some operators wait until the engine failure and shut-down checklist is called for before disconnecting the autothrottle. Others switch off the autothrottle as soon as convenient without specific reference to the checklist first.
Seems to me that if flying with one engine inoperative requires that the autothrottle be disconnected, then why delay disconnecting - especially as leaving the autothrottle connected can lead in to all sorts of trouble on one engine. Viewpoints please?