The purpose of holding full up elevator and max power against the brakes is to exploit the slipstream over the tailplane enabling a reduction of the weight of the nose wheel. You must remember though that the increased downforce from the tailplane ADDS to the weight of the aeroplane. As the aircraft accelerates the back pressure should be relaxed (not as previously described) trading off the increased downforce (weight) with the reduction of drag from the nose wheel. Holding full aft stick throughout will increase the take off run, not shorten it.
Holding full aft throughout the take off run prevents the aircraft becoming lighter and raises the angle of incidence towards the stall and increases induced drag. There has been much talk about being stuck in ground effect. Much more likely that the aircraft is stuck in 'the gate' of the imminent stall and an inability to lower the nose without setting back once more on the runway. All too often we read of aircraft impaled in trees along the climb path for this reason. Remember that an aircraft will only climb when power/thrust exceeds drag. Increase drag and the aircraft will climb less and to a point that it will not climb at all.
Homeguard
Very valid point! Pilots who hold the column back waiting for the aircraft to fly off are actually extending their takeoff roll. The only reason to do this is on rough bumpy strips where the pilot needs to get the nosewheel away from the ground. But it is another misconception that it is your quickest way off the ground.
I can remember flying a Seneca off bumpy grass and the aircraft launching off a particular bump before she was ready to fly. I was flying below the published stall speed. I believe another Seneca carrying a famous horse jockey crashed in a simular situation with a wing drop and subsequent crash killing some of the occupants.
Speed is your friend drag is your enemy.
Pace