For the NFL to work in that fashion, they would have to ban high and low tackling, as they do in rugby. I don't see that happening, especially as long as they allow blocking.
As you know, one of the reasons rugby works like it does is that there's no blocking, with the sole exceptions I can think of being in a scrum or maul, and there's a penalty for collapsing the scrum. The impacts in rugby, while often forceful, are almost always chest-to-chest or shoulder-to-chest and you don't see the kinds of open-field hits you see in the NFL.
I had thought about that, but believe that the lack of protection will change the styles of the players. Despite being a fullback on the pitch, I would not tackle football style, as I did as a safety.