Do AC inverter H bridges ever get driven this way?
Can it be done? Yes

Has it been done? Yes

Will it do as expected?  half the switching losses? Yes &amp; if care was taken over the right-leg device selection trading speed for conduction losses then you could further improve the powerCore losses. 

Quick model with some REALLY badly optimised output filter &amp; not really tuned, just to prove a point &amp; 100kHz switching freq (10kHz appeared to provide reasonable output but an FFT would be required &amp; varying loads: L,C, rect etc... ) 

Such a scheme does struggle at zero-crossing so the effect on THd would have to be evaluated and determined if it is an accepted limitation.