I agree mostly with the timing of leaving the team if the player is able to tolerate the team environment till the end of the season, stick it out and finish. The mid-summer phone call is not something I would recommend. Once the player returns to school the coach now has all fall and winter to "convince" the player she should tryout again. It could be a contentious issue for the player during the school year if they've made up their mind. Especially if/when the other players on the team find out.
Why lie to the coach? Come the next season when the coach asks why the player is not trying out they need to be told exactly why. If the coaches philosophies are running players away from the team they need to know that. Especially if tryout numbers are falling at the school.
If a player feels they are better than another girl on the field and think they did not get a legitimate shot to prove it they are entitled to that opinion. If they don't feel that way they should be playing rec ball.
The hard part comes when the other players ask why. That's when the player needs to have the short answer ready and stick to it.
There is no lie in what I said. That is a 100% true and repeatable story for just about every situation. And if part of those activities include running track then it wasn't specified but it is encompassed by what was said.
I don't see it as a parent and certainly not a student's job to try to educate a coach on why people are leaving his/her team. Especially after she has decided to quit. No matter what you say, it will be repeated as she was disgruntled because I played better players ahead of her.
I just can't see the good in telling the coach, after you have made up your mind to leave, that you think you are a better player then Suzy but Suzy got more playing time, especially if you need to have a prepared short answer for when Suzy asks you why you aren't playing.