Originally posted on 01/30/2018:

98% of players hold the extra ball. Easier to keep the rhythm and prevent turning around waiting on a ballboy.
The ball in pocket doesn't affect you one bit.
When I play matches I actually like to keep 2 extras in my pocket in case of a first serve let. Odds are when you hit a let it was a pretty good ball that just nips the net so you want to keep that same flow and duplicate that swing.