I think the saying goes something like
" rules are for the guidance of wise men, and the strict adhearence of fools"
I think the following incidence shows that there are times when it is wise to get the thing on the ground as soon as possible, but it also shows that being careful, which does not always mean slowly, with doing checklist is also important.
I believe crews have to be willing to adapt rules to suit the situation they find thenselves in. Note the engine did come off but appears not to have saved the situation
BOAC Flight 712 - Wikipedia, the free encyclopedia
Note it says the flight deck was reused on another B707, now that is what I call recycling