We are talking travel ball and a 2nd year 12U correct? While 12 players is great if and when you have everyone there, but IME players miss many scrimmages and tournaments for a variety of reasons (injuries, family vacations, sick, other commitments, a few kids changing teams after a couple of months, etc) and then teams are scrambling to field a team. Maybe its different where DD plays, but the players basically play 11 months out of the year, so having 13 on a roster still gives everybody an opportunity to get plenty of playing time.
Basing it primarily on my experience coaching one particular 12U team. We had only 10 players and 2 pitchers. Not saying that's ideal. It's not. But after getting away w/ 10, I sure don't think I'd want to 13. I'd prefer 11. Maybe we were fortunate, but players planned around vacations or other commitments. Or if I knew before making the schedule, I might plan around a commitment. Nobody ever missed a tournament. We didn't have injuries or sickness, although we were in metro ATL and part of an organization where if we needed a pickup player, we wouldn't have to scramble to get it. I can't recall using a pickup. We might've played w/ 9 a couple of times. We played tournaments 7 months a year, not 11. About 2.5 months off for middle school ball, 2.5 months off in winter (DEC through FEB).
Maybe it was just the situation we were in. I wonder if having 13 makes people more willing to take a weekend off. If you have 11 and they know they're going to play substantially, maybe they plan. We didn't want to just have 10. We wanted 11, which would've been a third pitcher. But never found the right girl.