It is a bit more complicated than that. If the shaft is perfectly straight, you can spin it to any speed without it whipping and breaking. That said, perfectly straight is a theoretical construct and impossible in real life.
So when you have a driveshaft that is damaged, an engine of most any size can break it.
Whipping (what you describe as a jumprope) is caused by centrifugal forces acting on an imbalance in the shaft.
The issue with high torque engines is that they can apply enough torque to twist the driveshaft tube itself, which results in small bends, making it out of round, leading to whipping from the centrifugal forces.
As it whips, it gets easier to bend, so it gets further out of round and the problem makes itself worse until the shaft fails.
