Efficient Single Phase Motor Speed Control
Motors are designed to cope with the torque variation from the mains frequency supply. A phase angle controller does not make this worse.

An integral cycle controller would lower the frequency of the torque variation. Say you fed your motor with 2 cycles on, one cycle off. It would judder at 40Hz. This lower frequency judder would be likely to cause damage.

Integral cycle control is just great for heaters, that take seconds to respond.