Why are the engines on the MAX and neo prone to bowing?
Rotor bowing is not unique to this generation of engines. It was an issue with the early IAE V2500. I remember initially they would have somebody manually rotate the fan some time after shutdown. This engine still has a longer start motoring period over the comparable CFM.

The root cause is simply making the shafts thinner, increasing their flexibility. When natural differential cooling occurs, they bow. This is done in the pursuit of weight reduction, which is important as new engines are larger and heavier than before.

The PW1000G is a special case, which is where the majority of the issues are occurring. Because of the fan gearbox, the fan operates at a slower speed than the core. Thus, for the same amount of power, the core will spin faster with less torque. The thickness of the shafts are only dependent on torque and not speed, so Pratt and Whitney was able to thin the shafts significantly and cut weight. Unfortunately, they did not properly account for rotor bowing.