However, in many other "what is it doing now?" situations the correct response is rarely to click out the automatics and fly the aircraft Usually a far better response is to go down a level of automation
Don't think so! One I see (and do myself) not infrequently is descending on automatics to capture glideslope, with localiser captured and glideslope armed. Looks good, glideslope coming in, then disaster!- you forgot the altitude window is armed, and because that captures before the glideslope, aeroplane levels off and thrust goes up, glideslope now rapidly falling away. Hands flustered, what to do? To me, the ONLY response is to hit disconnect, change configuration and slam throttles closed, otherwise you have lost glideslope irretrievably. The automatics will not now get you out of that one, so the use of 'rarely' in a not unusual occurrence is not suitable!
Another one- you have been vectored at a large angle to the localiser and passing through it. But you have been dumb and selected LOC arm. Now your heading control is locked into automatics, and you start making bizarre attacks to the Localiser from the other side and not able to control it. What to do? Best answer is to disconnect and fly it sensibly yourself. Then instead of turning out of control back towards the localiser at a stupid attack, you can manually control to a sensible and gentle attack.
There's 2 scenarios that contradict ' you should rarely disconnect, rather move down a stage'. Unless you do it rapidly and sensibly yourself, manually, you will probably not be able to recover the situation satisfactorily. It's the younger pilots who let automatics fly a serviceable aeroplane into the ground while they faff around with the MCP. Us older experienced pilots know when we can do it better!