This is not an additional restriction, it just makes sure the parents or at least an adult helps guide the young woman through a very difficult time. You know parental permission is not such a crazy thing here.
Minors need permission to get their ears pierced. So then why all of a sudden do we think a young woman who already displayed a lapse a good judgment will make the right call when it comes to abortion? I do support the provision (that is found in most if not all of these laws) to get permission from a judge instead of parents, in situations where the girl can reasonably suspect physical abuse from her parents due to the request.