Don't confuse cogging with torque pulsation.
Cogging can only happen with iron cored machines.
All single phase machines have torque pulsation. With 3 phase machines loaded conventionally with normal loads the instantaneous sum of the 3 phases is zero so at any instant the torque of each phase is balanced and the thing should be perfectly smooth. If waveforms are not perfect then there may be a minor torque pulsation normally at 3 times frequency but it is small. When you use strange loads such as rectifiers then there may bit of extra pulsation but it will be tiny compared with single phase.
Single phase alternators all tend to vibrate but with conventional machines with large rotating mass and high speed small machines at least survive perfectly well.
With wind machines operating at low speed and over a wide frequency range the vibration from a single phase machine can be very destructive and if you hit mechanical resonance it may be bad indeed. You will have noise and vibration problems that you may find hard to live with and a common problem is shaking the tail to bits.
Single phase has no other advantage whatsoever to compensate for these bad characteristics. It works very badly with rectifiers and the efficiency is lower and the alternator needs to be bigger for the same output.
These axial machines are not wound as true 3 phase machines so there may be marginally less gain from 3 phase but typically a single phase machine needs to be 50% bigger for the same power output.
3 phase machines often growl or hum on load but this is caused by the tiny torque pulsation that will be only a few %. Some find this noise a problem under certain circumstances. Try single phase and you will find it hard to live with a real full torque to zero pulsation every cycle.
Flux