I think that you should be fair with all your players. You need to utilize all the talent on your team. If you do not plan to use that player, don't let them sit in the heat on the bench for five games in a tournament. Cut the player loose for whatever reason.
Thank you for your comment. I agree with you that you should try to utilize all of the players on your team. Not necessarily equally, but sufficiently so that everyone feels they are a valued member of the team.
I say this assuming everyone on the team is putting in effort at practice (especially attendance) and other team events. So, if a player is not making it to practice, I do not think it is fair to the players who are working hard at practice to try and sacrifice playing time to give it to those who are not making it to practice. It is a give and take thing. Players should be rewarded for giving effort at practice as well as the tournaments/games.
Practice is also a time when coaches should be working hard with ALL of the players so that they do feel comfortable playing them. Players need that confidence to be successful, and practice is where they have the opportunity to earn it.
If, however, you have a player that you never plan to play, then the player (and her family) should not be put through those endless hot summer weekends watching everyone else play. They should be, as you put it, "cut loose". That is only fair to the player, player's family and in the end, the entire team.