I was not advocating that only one ball could be on the table. But, if you play that balls could be jumped of the table when pocketing the ball in your opponents hole....then I suggested that you play using the one and stop rule, so the player who needs two can't simply run out and win the game.Yes, that's why the name, "Sudden Death" One Ball One Pocket -- to differentiate it.
That is an interesting idea. I like it better than Mitch's Philly One Ball One Pocket ("Bare Ball" I think they call it). And better than the way they played it at Southern Rec. What you are talking about is basically One and Stop applied to One Ball One Pocket. But I'm not sure why you would need to add that additional rule, other than some people's obsession with the idea that since it is called One Ball One Pocket, there should never be more than one ball on the table.
You can limit fouls and play standard One Pocket (starting with only one ball of course), and that works fine, and you still get plenty of spot shots -- every time there is a simple pocket scratch or foul without a ball pocketed on the same stroke. So what if there might be 2-3 balls on the table. It's the true end game of One Pocket -- what could be better than that? The only reason to even have any foul limits -- whether Sudden Death or if you are limited to needing two balls -- is just to keep the games short. That would be mainly for tournament play I would think.
My rational for suggesting this is that the OBOP game is won by pocketing the ball from wherever your opponent has left you. Allowing a player to play position off of his own shot and run two balls is a departure from that scenario and does not fully penalize him for his previous foul, and obviously favors the better shooter.