I think it needs some mechanism to keep it from going on indefinitely. Yes, sure, you can say that someone will get tired (or bored) enough to finally lose 3 in a row, or just quit and forfeit - but that's not a very interesting way to go about things.
Now - you didn't specify WHICH game you would be playing under this scenario...but assuming you are talking about 8-ball, you could go with your rule until someone gets to 10 games. After that, rather than 3 games ahead, you could play for 10 balls ahead - for example. After 20 games, you could reduce it to 5 balls ahead. After 30 games - it's whoever is ahead by the 40th game.
Personally, I can't play 8-ball or 9-ball for more than about 6 or 7 games before I get insanely bored anyway. So count me out