Yes.
The kids that have been there since day 1 play under rules of the league, and rules do not disallow the coach from this action. The players (and, as an extension, the parents) should be aware of these rules. They could perform better.
A coach telling a player that he isn't performing well enough should be a beneficial lesson for the player. A motivation. A spot on a team does not entitle a player to anything more than a chance. The coach is abiding by the rules of the league/tournament in which the team plays and if a player doesn't like it, then the player shouldn't play for that team. Or, get better.
I know all that may sound harsh, but baseball is pretty harsh sometimes. I don't mean to be harsh, I'm just being realistic.
I find this attitude, especially at the 13/14u level, mind-boggling.
You're aware that it's pretty routine for teams at this age level to wrap up their season with a "destination" tournament, right? So, hypothetically there's a team that has a kid who's good enough to be the starting SS, paid a 4-figure sum to be on the team, kid worked hard all year and had a great season, and his family booked a vacation around the season ending tournament. Coach then decides to bring in a replacement for the kid for this final tournament, and tells him he'll be the backup for that tournament, and you expect both the kid and parent to be OK with that? What if you're the parent in this hypothetical, and you're the one paying the bills?