First of all, the NCATA is governed by USAG because the skills that have been infused into cheerleading since the early 70s are the same skill sets that gymnastics is made up of. And the fact that the NCATA doesn't use a sprung floor is whole other argument, doesn't make it right.
I stated this because A&T is closer to cheerleading than Acrobatics so using the USAG rules for A&T makes more sense than what you stated for the Acro ones.
In my personal opinion all competitive cheer should be performed on spring floor. Telling a girl that she should follow FIG standards for her cheerleading does not achieve this and for someone who isn't familiar with gymnastics governing bodies probably makes no sense.
You could argue that performing this skill before she is ready could result in a serious head injury. Figures and studies are a great way to back that up.
Your understanding of critical height is correct. However, the athlete doesn't not need to jump 4ft for their head to be at a height of 4ft. Every athlete that is taller than 4.5ft has their head above critical height without needing to jump. They don't need to flip above critical height, but at a point in the jump their head reaches that height.
So does this mean that basketball is a sport that is too dangerous to perform? 6 foot men on a hardwood floor certainly are in a grave danger of a serious head injury? or soccer? (grass only has a critical height of ~4.5') or figure skating? or any unpadded sport you can name?
I think this measurement could be very useful in determining safer rules. However, I don't think it accounts for many other factors and I think a better measurement could be found.
You are correct, the cheer industry rarely uses science when coming up with rules.
I don't think it is often the basis of the rules. However, I have noticed a great trend in using studies when forming new rules which is a step in the positive direction. (Ex. elimination of double downs in high school)
Sorry to anyone reading for hijaking this thread! I would love to start a thread on science, safety, and cheerleading rules to discuss this further... because it is a great topic that needs to be talked about. So I won't reply here anymore :)
I truly respect what you are doing at the National Cheer Safety Foundation, I just disagree with some of the things you promote/say.