I'm not a very skilled player. All I ever do with my left hand is specify chords (and usually with just 1 or 2 keys pressed.) So I don't use the left voice personally.

What I have found is that many styles have a "pad" track, usually in an advanced variation, which gives the same effect as playing full, sustained chords with the left hand. A lot of the organ music I play sounds best with ONLY this track and the bass track activated. Combined with sync stop, I can almost fool non-musicians into thinking that I know what I'm doing!