My brother's youth baseball team recently played in their league championship game, and it was ridiculous politics and favoritism that likely cost cthem the game. The starting pitcher was the coach's son, and while he is a good pitcher, most starters in this league (middle school aged) typically do not pitch more than 3-4 innings. His team held a 3-2 lead, but despite having other good pitchers that he could have used in the later innings, the coach's son continued pitching into the 6th inning, and was not finally replaced until he had allowed 5 more runs in that inning and recorded only one out. My brother (who had struck out 7 in three innings in his previous pitching outing) was finally brought in to pitch, and finished the inning without allowing any more runs, but at that point it was too late, because although his team scored twice in the next (and last) inning, they lost 7-5.
So yes, even in a league such as his, where the primary objective is to give everyone playing time, problems can come up when a coach decides that he wants his son to be the hero in the big game.
"Too many pitchers, that's all, there are just too many pitchers Ten or twelve on a team. Don't see how any of them get enough work. Four starting pitchers and one relief man ought to be enough. Pitch 'em every three days and you'd find they'd get control and good, strong arms."