The situation changes somewhat when there is a significant spread (e.g.10-15 knots) between V1 and VR with engine failure while the aircraft is still on the runway. Of course we can only use the simulator as an example, as information on real engine failures at V1 is practically non-existent.
In the 737 at least, there is a huge difference between the stick force to rotate the aircraft all engines and that of rotating following an engine failure on the runway
Since the vertical component of thrust is halved with engine failure, it takes a much harder and prolonged pull at VR to get airborne since the stab trim setting is set for a normal take off; not a single engine take off. In the simulator we see pilots often rotate much more slowly with engine failure on the runway. This is not done on purpose but because the stab trim setting is now invalid and a much heavier initial pull is needed to get the nose up off the ground.
It is common, in fact, to see pilots inadvertently allowing the aircraft to skip back on the ground during rotation because the slightest relaxation of stick pull caused by momentary surprise at the amount of back pressure needed, slows rotation rate; especially when passing through 10 degrees nose up when the aircraft always seems to hesitate momentarily. It used to be called the "two step rotation" and happened to the 727 as well.
Because of the risk of tail-strike, it is prudent to avoid using any stab trim to help with dragging the aircraft clear of the ground. One therefore has to manually "muscle" the aircraft to the desired 12-14 degrees climb attitude before relieving the heavy stick force with stab trim at about 300 feet where there is no chance of tail strike.
Also with engine failure at V1 and continue to VR, as far as I recall and providing rotation rate is correct, V2 is reached by around 35 feet and the climb continued at V2. Different on two engines of course where V2 plus 15 to 25 knots is reached by the time the aircraft reaches 15 degrees body angle.