Why do we need 3 phase power supply?
Comparing 3-phase with single phase transmission, 3 phase has a couple of significant advantages:

1) More efficient use of conductors : given the same peak voltage between conductors and same current in each conductor, 3-phase delivers 3x the power with 1.5x the copper (3 wires instead of 2). This doubles the usefulness of each pound of copper (aluminium etc) Over long distances, this is a significant cost saving.

2) Three phase motors run smoothly with no additional complexity to define their running direction. Power delivery is approximately constant as the rotor follows the rotating field (with some slip, in an induction motor) with no torque variation or vibration. Reversing can be as simple as interchanging any two phases.

The advantage of smoothness also applies to the 3 phase generators : they absorb power from e.g. the turbine smoothly : a large single phase generator would probably be shaken apart from the torque variations.