You don't see the problem with "I don't like sport A, I like sport B. Make sport A more like sport B"? The pauses lead to a more rigid tactical game (you can't really run set plays much in rugby as you do on most downs in football). And the physical violence padding allows is also part of the appeal of the game. Just google "Clowney hit" and you see thousands of people losing their minds in praise for a hit of the kind you'll never see without padding.
Of course, the second point is more what this article is about and I believe American football will eventually been seen like we view Roman gladiators. But for now, padding is a major reason why it is the biggest sport in America.