Phase shifting is rather difficult, so you'd tend not to do it in general. For wideband applications, say: you need a flat phase shift over the whole band.
When you do have a variable phase shift, and maybe can take advantage of harmonic distortion in the output, i.e. to improve efficiency while filtering it from the output signal -- or don't care at all -- yes, that's doable.
I'm not sure if that's done for RF, because the load varies -- you're going from 100% common mode, to 100% differential mode. If the load is differential only, then the finals are perfectly unloaded when in phase. Which isn't going to do your efficiency any favors, but might blow them up, too (if they're no good at handling SWR). If you have some way to recycle CM, yes, it would be usable, and efficient.
(RF of course has the better solution of phase modulating the carrier, and amplitude modulating the finals -- you can do PAM explicitly.)
For power switching, it's quite practical and abbreviated as PSPWM. Again, when in phase, you have full switching but no load current, so the inverters are hard switching just their capacitance, for all that power dissipation and no output. Not the greatest situation. And, not only does hard switching increase EMI, but the fact that you're explicitly driving 100% common mode into the load helps even less...
Tim