First things first: Search function, JONG!
As for the purpose of the pole plant, tell me where your hands are when you're skiing if you're not using poles. Do they go to your sides? I would guess yes, based on the comment about having a dropping hand, even with poles. That tells me you're probably not using your poles properly for timing the turn. If your hands go to your sides if you don't use poles, then that tells me your weight isn't properly distributed fore and aft. It's likely that you'll be in the back seat if you aren't using poles, especially if you're letting your hands drop. If you don't keep your hands in front, you'll be in the back seat.
Again, as noted above, the pole plant is about timing. It's what initiates the turn and using proper poling technique is what establishes good turning rhythm. Also, on groomed, relatively flat slopes, turning without poles can be fairly easy as you lay your skis over edge to edge. But on irregular and/or steeper surfaces, initiating turns with pole plants really aids in turning where you want to, not where you happen to.
Edit to add: I should have noted that they're especially useful for skating across flats and for whacking belligerent people in lift lines.
My hands are out in front. Sometimes they are forward and moved to the outside of the turn to help with counter balance, sometimes rhythmically moving in time with the turns, but always forwards (except when I'm coasting straight through an empty lift corral to the chair).