The other difference is rugby limits the contact to the guy carrying the ball to a greater degree than American football. In the US version, the majority of players on the field will have contact on the majority of plays.
In fact the disease most discussed and studied has been Chronic Traumatic Encephalopathy or CTE. The position most likely (nearly 50%) to be affected are the linemen[1], not the guys leveling or receiving the bone crushing hits, but the guys doing the hum drum blocking on every play.
The positions reporting the most concussions though are the guys who are doing the hitting and being hit, the guys with the ball and tackling him[2]. But these guys get the big hits rarely as players are subbed in and out and the ball is given to different players all the time. If they get a concussion it is obvious and are usually pulled from the game.
Linemen on the other hand, are consistently in every play, and are blocking on every single play. They may be getting minor concussions every play, but not something noticeable enough to be pulled from the game.
[1]https://www.si.com/nfl/2017/07/25/boston-university-study-ct...
[2]http://apps.frontline.org/concussion-watch/#positions_2015
This actually means there might be hope. The game could be modified to reduce the impact on the linemen. Reduce the distance the defense has to back off from the line of scrimmage, maybe even right down to zero or even a straight-up scrum. No lead-up to that first hit, they start out in contact. No lunge forward to close the gap between offence and defense.
Same gameplay happens - two lines of men trying to break through/protect the QB, but without that initial impact because they're already in a wrestling position.
That said they cant all of a sudden change the gear but they can evolve the rules to adapt.
Players are bigger, faster, and more powerful because that makes them better players. Not because equipment has evolved. It's the training of the athletes that has evolved.