Yes, it seems as though this is an avoided subject and a privately held secret. However, I will jump in, nonetheless.

I started with the organ many years ago and am used to playing with sound on both hands. I know, however, many in split keyboard mode, excluding manual bass, use the left hand used mainly for chord designation and button pushing.

To me, there are pros and cons. I don't simply hold a sustaining chord, but work it in many ways from leading to the next chord progression to comping brass. Obviously, the chord memory is there to allow one to lift the hand with no interruption to the style, freeing it up. If I use piano, no problem, but organ sustains, making it trickier to interrupt without being noticeable.

OOH when I use a busier accomp, I suppose I really don't need LH sound, but I remember the original brass stabs, e.g. and it adds authenticity. One thing is sure, and that is I wouldn't have to pre-plan registrations as much If I didn't strap my LH to the keyboard, but give up some sound.