TR wasn't masculine for the simple reason that he wasn't a man. He was a boy.
All "national greatness" types are essentially adolescent boys.
That's because they don't really dream of national greatness. They dream of personal greatness, with greatness being defined as being the star of their own comic book. I don't think you can underestimate the impact of the "Buffalo Bill" style popular culture of newspapers and pulp magazines in the second half of the 19th century, and their role in producing Hemingwayesque personalities like TR and, well, like Hemingway himself.
They wanted to grow up and have people write pulp stories about them, like the stories they read about Custer and Wyatt Earp. All of the rest of it is rationalization to that end.
But at least TR and Hemingway actually... did some stuff.
As I wrote before, once upon a time the Glenn Reynolds types wished they were Captain Kirk. Now they wish they could live on the holodeck.