So I do not think your data means what you believe it means. There is a reason they call NFL "Not For Long".
I would not let my children play either American football or rugby, existing options like basketball or tennis. Luckily most of the world plays soccer.
> For each of the sports, they looked at concussion rates based on minutes of athletic exposure (AE), which includes competitions or practices with the potential for injury. The overall concussion risk across all of the sports included in the analysis was 0.23 injuries per 1,000 AEs. By comparison, the concussion risk per 1,000 AEs for rugby was 4.18, while it was 1.2 for hockey and 0.53 for American football.
https://www.reuters.com/article/us-health-concussion-youth-s...
So on the one hand: research.
On the other hand: soccer (especially with sense enough not to be hitting headers all the time), has stupendously less physical contact than rugby or "football"... how could it be more damaging/dangerous with less contact?