There are advantages and disadvantages for different phase orders, but two advantages of 3-phase are compelling: Zero common conductor current when balanced and only one more conductor than minimum needed to complete a circuit. In the early days it was competing with 2-phase, which shares the advantage of providing a rotating vector but with more torque ripple and the severe penalty of requiring more copper to transmit the same amount of power at a given voltage.
High order systems were better for rotary conversion and rectification with single-polarity rectifiers, e.g. a mercury arc (always common cathode) required 6-phase AC to give 6-pulse rectification, therefore a zig-zag transformer was used to derive this from a 3-phase supply. But with ordinary motors do not benefit from the mirror-image phases, and bridge rectification only benefits by reduced harmonics on the AC side and slightly lower ripple.
We have Ferraris and Tesla to thank for inventing polyphase systems in general and Dobrovolsky for making 3-phase the system of choice.
