3-phase offers enormous advantages for industrial applications (see http://www.quora.com/Why-is-power-transmitted-in-3-phase) over 1-phase without needing an enormous additional amount of infrastructure and wiring. In particular, 3-phase can be carried on three wires with an optional neutral that doesn’t bear much current load. This is not the case for 3-phase motors which do not require it.
The 3-phase motor design is already ideal because the power output of all three phases is equal. This means that all your motors will be driven with constant torque and no AC frequency components. Motor design can be simplified because 3 phases define a direction of motion while 1 phase doesn’t.
6-phase or 9-phase would require 6-7 or 9-10 wires, respectively, and in most cases there is not really any good engineering advantage for needing 6-phase or 9-phase. In addition, by rigging up that many wires you also increase the potential for failures of various sorts, including short circuits and broken lines. You might also get people on legacy equipment using only 3 of your 9 phases which throws off your whole balanced advantage from the power infrastructure perspective.
For most applications, 3-phase is not necessary. In many ways, it is “ideal”. It isn’t true that “more phase is better”. This is similar to how tripods have clear benefits over monopods. However, a tripod can do nothing useful for your photography. A tripod is already ideal. 🙂