Why do 3 phase motors not need a neutral?

Three-phase induction motors do not need a neutral because they are a balanced three-phase load.

The balance current in all three phases of the motor leads to no current in the neutral.

Therefore, there is no need for neutral in the 3 phase induction motor.

Even in a Y-connected motor with a common point, the motor is an inherently balanced load:

each phase is the same number of windings and wire size and pulls equally on the stator no matter how much load is on the rotor/shaft.