Yes, girls should wear short shorts. Personally, it is my thought that anything longer than the tip of the middle finger is too LONG for men or women, boys or girls. As long as there's not butt cheek hanging out, I have no problem with it.
There is a caveat. If you are not fit, but heavily obese, please, do not dress up in short shorts, they do not look good on you. I like my shorts four to five inches for outside, and casual short shorts for around the house and I'm a straight adult male, so there is nothing wrong with them. And, considering that, a few decades back, they were the norm for men and women, we ought go back to that sense of body freedom.