There is IEC 60309, but those are too bulky to be practical for home use. Three-phase power is basically only used for permanently installed equipment, like an electric stove, heat pump, car charger, or solar panels.

How is 3-phase better for rectifying? Is it because it's easier with them 120 degrees out of phase rather than 180?

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.