In addition to everything Homerun04 wrote, it may also depend on the event. For instance, when 2B's team went to East Cobb and other scouted tournaments this summer, they went to win, so there was not equal playing time. Starters had to earn their spots over time. But when we have been to showcases where they do skills evaluations then have "games" that have special rules (no walks, only a certain number of batters in an inning, etc.), like PG underclassmen, so far everyone has gotten equal time - at least that's the way it seems to me. Then again, that's not really a "team" event.
On the other hand, what your coach said doesn't sit right with me. How does he determine who plays best? Stats?