This is a really big decision and should not be left up to the player. The player will always want to play up. But, is that really going to benefit their development on the field. I do not believe any player should be playing up until they are 11/12 years old and here is why. First, the gross motor skill that is needed to play baseball and develop is not something that comes quickly. If the player is pushed up too fast they are not able to learn the fundamental movements that are needed to be successful. They will focus on the outcome and not the process. The process of hitting, throwing and catching. Second, when you push a player to play up the game can move too fast for them leading to habits that will only result in slowing down development and enjoyment of the game. Last, and in my opinion the most important, is why are they playing up? Are they moving up to hit last, run the bases, or get walked because they are smaller than the rest of the payers? The purpose of youth development is to allow players to develop at their own pace and feel success before putting them into a situation where winning is the main goal of the team.
The goal of any coach is to ensure development. That looks different for each person, but if the player has the ability to play at their own age and be the lead off hitter, or play every game, or be allowed to fail without fear, the growth of that player will only benefit their playing career for years to come. At the youth level it should never be about the results. The only thing that matters is learning how to play, how to deal with failure, and how to develop the skills through a process focused approach and not the results.