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.
I do something similar, and often I will revoice the pad to another voice (organ e.g.), or, I use Style Creator to put that pad in less advanced parts of the style.
Also, any rhythmic parts (chord 1 and 2 and Phrase 1 and 2) can also be subbed into other variations, but, simplest of all is using the pad as you described.
Ian