I disagree with the bolded. James Harrison might act like that, but the majority of players are aware of the rules designed to promote player safety, so they will/do "pull" back if possible. You have players with the hard-nosed, "I'm going to murder the opposing team" attitude, and you have those who just want to win and do it fairly. Who knows what the actual numbers are, but a lot of players respect each other and enjoy playing with and against each other.
All it takes to win is preventing the other team from making plays. This could involve taking them out of the game, or just being better than them and preventing/stopping plays. The Saints went so far as to name specific players to "take out".
Harrison is/was a phenomenal player, but a poor example when we're discussing concerns for player safety.