Coacht, those shorts you show in the picture are the exception rather than the rule. While some are short, many teams have spandex with at least a 2 3/4 inch inseam and most are longer than that.
I have seen basketball shorts come off....because it happened to my daughter. Luckily she had on underwear. It was her fault that she didn't tie them, but you have to remember that you are dealing with teenagers, and girls in particular.
I had much rather have my kid in spandex than basketball shorts. Go to any pool, lake, or etc. (and some malls) and you will see things much more revealing than what you show.