Let's put a little spin on this one by age group:
Younger age groups, you picked her to play, so obviously the kid has something. You are the coach to help her get better. If you are going to put her in and immediately pull her out on a mistake, that defeats the purpose. Everyone makes learning mistakes. Also, how are they going to get experience playing in the games including big games if they go in with a fear of being pulled at a quick mistake. (See this all the time in Bskt-Ball) had one coach tell her at a young age "she knows her role"... Funny that particular coach never told the girls what their roles were.....
By the time they are in their higher teens, the teams are usually picked on quality of talent and the playing time is usually shared across the board. Playing-- in particular catchers, in multiple high quality games on a 90 degree day, does take it's toll and breaks on some games help. I can honestly say we have been very happy with the time played each year since she was 14.... Making a jump she did from 14 to 18U was a great learning experience for her and she did exactly what was asked of her at that time-- less playing time due to the more experienced players. But those players also helped mentor the younger ones that year. Playing other positions that year also helped her become a well rounded player and at the end of the day, it is a team sport, so do whatever is asked to help your team succeed and it pays off in the end in sports and life......
Yes we pay to participate in travel, but playing time is determined by a multitude of factors.. Especially the coaches, that's why you need to do your homework on any organization before jumping in with two feet.