It would be silly to say that there could never be a deal breaker. My point of view is that parents seem to want to smooth out all of the edges for their daughters and break commitments for reasons that are more in the category of fairness than any real issue of safety or well being of the child. In this respect, I would consider this a snowflake approach to parenting and a participation trophy mentality. Not my idea of what sports can teach children. If you do it right, participation in sports can help your kids get a leg up on life. If you make it too easy, fight their battles for them, fight for them to always have a fair shot at everything --- they will not learn how to handle adversity and you may as well be prepared to go on job interviews with them, chaperone them on all of their dates, and have the college coach on speed dial. Your daughter will love that level of involvement I'm sure...
BTW, my parents probably thought that I was too easy on my kids! My parents were tough. I could be on any team or activity but I had to be able to get there on my own (walk, bike or bum a ride). When I was upset about not getting enough playing time on the local little league team when I was 10 years old, my Mom made me go talk to the coach - I was not allowed to call him and she certainly was not going to do it for me. It was probably the hardest thing I had to do up to that point in my life. She also made me practice with her and my dad taking turns being the coach (first experience in roll playing which has turned out to be a valuable skill in my life). I went to the coach - he was a mean SOB and even his own boys thought he was a jerk. I'm pretty sure that he told me that I should probably be looking for a sport other than baseball that I might someday be good at. I did not get any more playing time that year. My dad would have skinned me alive if I had quit the team because, "we are not quitters in this family". The point is that by the time I got to high school and suffered through a wrestling coach who really did not like me (and it was mutual), I was thick skinned and confident. I did not need his love or his support - I made the lineup because I put out all of the competition in my weight class and a few others just for sport! Most of them eventually recovered from their injuries. I learned how to be ruthless, how to lead others and how to fight through the pain. In truth, I learned more from playing sports than I ever did from any classes in school, including in college. It has served me well and in turn I made sure that my kids learned most of the same lessons and they are doing well for themselves too. That's is what it is all about!