I think this variant would only work if either nobles replenished, or you were prevented from getting more than one noble. Otherwise it's possible to have someone get to 15, but be unable to get a noble as they've all been taken already.
Agreed, I like the choice of whether to go for a noble or not. Playing this way removes some of the choices from the player and makes it easier in some cases to prevent a player from being able to win the game.
Also, I think in about 15 games, I have only seen one win where the player didn't have a noble.