Protection gear

[Ryoga Hibiki]

Question, as I don't know much about american football but I love rugby.
I can see that the hits in the football are definitely more violent, and I can see some of the reasons (different technique allowed, the possibility to hit someone off ball, the space the forward pass opens up allowing for more build up of speed and unpredictable angles).
But don't you think that the presence of all that gear makes players more reckless and give them something harder to hit with?
Could it be true the paradox that the game would be safer with less protection?