"Early football was a violent game, with few rules and much pushing, punching, and piling on. Serious injuries were common. Early in the 1900's, President Theodore Roosevelt threatened to ban the game unless the violence was lessened."So that gives a little of the context of what was then a major controversy. In this passage, Chesterton simply uses the controversy as a springboard for another point of his, but I did want to give some information on the controversy so the first part of Chesterton's passage would be more intelligible
Of course, I do not off this as a judgment pro or con, on the question of American football. Like Mr. Carnegie, I have only seen American football in photographs. And, unlike Mr. Carnegie, I do not think that sufficient ground for forming an opinion. It may be, as some say, that American football passes the limits of legitimate risk of life; and that is a matter of morals. But in so far as it consists in people being rolled over and over, I think it is not merely harmless, but beneficent and beautiful. I think it would be a good thing if most of our great public men could at some great and public occasion of their career be solemnly and ceremonially rolled over and over. I think it would be a good thing if all philanthropists could be rolled over and over. I think it would be a good thing if Mr. Carnegie could be rolled over and over. I do not merely mean that I or others might enjoy the spectacle with an inhumane mirth; I mean that it would be a good thing for Mr. Carnegie, and would add what is lacking to his many fine qualities. For the two things that are lacking in nearly all philanthropists on earth are these two- laughter and humility. And these are such great springs of human happiness that I feel sure that Mr. Carnegie would thank me for having gradually awakened them in his soul, even if I did it by rolling him in a barrel down Primrose Hill.
-December 29,1906, Illustrated London News