You always have power available at any instant. The capacitor is only for smoothing the ripple, not holding energy while none is being delivered. 3-phase motors just work too.

https://en.wikipedia.org/wiki/Rectifier#/media/File:3_phase_... shows the visual of what full-wave 3-phase rectification is. Note how very low the ripple is between the high and the low of these peaks.

3 phase is 120 degrees out of phase. Wall power only has a single phase, 360 degrees. Via +/- rectification the situation gets more complex. The key thing, as the other commenter points out, is that there is always always power available. Where-as with wall-power you literally drop to zero voltage as you go + to - & back.