Now, if we look further back in time, we come to the old B707-320 straight-pipe (non-fan, for you new folks) airplane.
At very heavy weights (and yes, this was the first
heavy jet), if an engine (especially an outboard engine) failed just as the rotation maneuver began, one had better be very careful with the continued rate.
Large heading changes with that failed engine were a distinct possibility, as the rudder required an almighty push (nearly 150 pounds worth) to keep the airplane reasonably straight.
And no, I'm not so old that I flew these airplanes when they were new, but instead had been passed on down to ad-hoc charter carriers, after they had been worn down to very tired machines...ex-PanAmerican and TWA airplanes, mostly.
The result...pilots normally did a quite slow rotation at heavy weights, to be absolutely
sure that the swing toward the failed engine could be countered, as the performance with these very early Boeings needed to be seen to be believed.
DP Davies was absolutely right to have challanged Boeing to modify the 707 rudder hydraulic power system...and for good reason.
Flying old TriStars today, at heavy weights, the same slow rotation is used.
When First Officers ask why, I tell 'em...you gotta keep it
straight if a wing engine fails.
In addition, if a rapid rotation with these tired old airplanes was tried at heavy weights, and an engine fails at the most critical time, you could find yourself at V2...and then watch the airspeed start to unwind.
This is
not good, as then your climb rate (if you manage to have any left) goes straight downhill.
In these cases, a little extra speed is your friend.
Now I would expect that some of the new(er) pilots here might have a doubt about all this, with the newer generation of airplanes, but these are the facts with the old large heavy first generation jet transport airplanes.
Especially, the B707.