Most high school cheerleaders are not in shape enough to safely perform these skills. Add int he fact that many schools don't have safe practice set ups (proper mats) and it's a recipe for danger. That's why the rules that are in place are in place.
I do feel that not only a required safety cert for all coaches (only mandated in some states) is necessary. In addition, I'd like to see HS go toward a level system. Not necessarily 1-6 like AS, but I'd like to see a novice, intermediate and advanced. There are set skills for each level and you'd have to "test out" of a level before being able to move up to the skills and be able to compete in the next level. This could be accomplished by NFHS certifiers going to camps and schools over the summer and signing off on a teams skills in tumbling, stunting and jumps.