Hi Star,
It comes from playing an arranger keyboard. When I only played piano, it was almost all classical with only a few popular tunes. I originally got an arranger as a cheap midi controller but discovered I was an organist after all. I found that playing the way I described was good for getting the accompaniment going. Once you have played a chord, the accompaniment follows it, so you can play any old rhythm in the left hand provided you don't change the chord until you are ready. This is also the reason why I don't use the panel organs which don't have touch response. I like to play the left hand a little quieter so that it doesn't overwhelm the right hand.
Bryan