The biggest problem with new balls is that some of them get slippery.
One way to limit the number of times the home team pitcher asks for another ball is to take the one she doesn't want out of the game (it must have something wrong with it) and ask the home coach for a new ball, which you then give to the pitcher. The coach will then deal with the pitcher.
I have had pitchers want a specific ball and slow the game down asking for it back if it gets hit out of play and is then returned.
I have only seen one pitcher who checks the ball every time she gets to the circle and ask for a different ball if she doesn't like it (before a warm up is thrown). Most just don't know the rule.
I always look at the ball if a pitcher asks for a different ball, in some cases there actually is a problem (the ball is cut or a seam ripped).