Having started as a piano player I am a believer in making best use of both hands to play the keys. So using a style the LH can be used not only to define the chords but to add an extra accomp part of its own via having the left voice on and choosing appropriate inversions of the chords, so there is a logical "musical movement" (that's my story!) to them. Examples of left voices would be strings, or a guitar, the latter useful for accompanying a solo voice in the RH. The most use I make of the LH voice is for BigBand songs. I feel conventional BB misses that interplay between the different sections in a real band where say two thirds of the band plays melody while the rest will respond to varying levels with supporting accomp and brass stabs. For that I use a custom voice in the left which plays ensemble saxes (because of the chording) which when higher velocity is used brings in upper octave brass as stabs or longer accompaniment notes.
Having done that for some years I now feel there is a definite "hole" in the arrangement if I don't use the left voice! You can to some extent use the style parts to cover but they are severely limited in flexibility, and in any case the more prominent you make them, the more obvious their repetition becomes, something you can guard against if you play the more prominent accomp. yourself.
John