I actually just looked up the most recent studies and most have concussion rates in Rugby equal to or slightly higher than American Football (Rugby 3/1000 players per game, football 2.5/1000 players per game). Most of these injuries happen from whiplash to the ground rather than head on head contact apparently so the classes of injuries are different between the two sports. These numbers were also derived from college athletics so do with them what you will. Odds are due to the increased strength and speed of pro football and rugby players the rates increase. For example in youth football the rate is 0.53/1000 players per game and youth rugby actually increases to 5.5/1000 players per game so there is no telling what the pro rates look like.This is interesting because I know earlier studies contradicted these findings but that is how science works.
That being said there is a lot of work that has been done examining concussion rates when players go helmetless in American football and the results are undeniable. In game concussion rates went down 28% for players in a University of New Hampshire study who still played with a helmet in games, but participated in helmetless tackling drills in practice. I think this could be the key. Players can keep their iconic headgear on in games, but are drilled in tackling without helmets. This would actually encourage the "textbook" heads-up form all coaches preach and would probably result in better defensive play overall while also decreasing in game concussion rates. We all complain about how bad tackling is in modern football. Helmetless tackling drills could address concussions and degrading fundamentals in one go.
Here is an interesting article on the case for no helmets:
https://archive.thinkprogress.org/c...ts-actually-make-football-safer-75393ffe5c32/
Personally I would be all for altering helmets to achieve a safer game that maintains its physical nature. No one would argue that Rugby is soft and they don't wear helmets so I see no problem in exploring alternative head protection for American Football as long as the game stays true to its form.