TR's tough guy image was the result of a huge PR campaign... carried out by him. He was his own publicist, more or less. I mean, he commissioned a fake ass painting of him valiantly leading the charge in an imperialist, expansionist war.
https://www.history.com/news/teddy-roosevelt-american-manliness-rough-riders
I read this book in grad school and there is a whole chapter dedicated to ol' Teddy
Like the History Channel article notes, the guy had a strange mix of racial and gender anxiety. He was obsessed with manliness and conquest, so he constantly argued for US expansionism on the grounds that the civilized white race had a duty to spread civilization throughout not just the continent but the world (Hawaii and the Philippines by this time)
He's regarded as a great president because both liberal and conservative historians see no problem with American imperialism. So the US should rule the world, they just disagree on what method is best.
His reining in of Gilded Age cunts is undoubtedly a positive though. So he gets a B- from me. Good but not great.