TR was wildly popular and could easily have won a third term in ‘08, but he had promised to step down after two, and he honored that promise. He was disappointed in Taft, so he ran again in ‘12.
He only won just one term in 1904, but served the bulk of McKinley’s term. Had he run in 1908 instead of Taft, undoubtedly he would’ve, rather than his cousin, established a “Presidency-for-Life.” I believe he was a singularly unique war fetishest (perhaps the one and only President in the history of the Republic to have such a fetish) and would’ve charged off to intervene in the War in Europe the day after it broke out (indeed, WW1 was probably one war we could’ve easily stayed out of with little difference in the outcome — unlike WW2 and Buchanan’s bizarre fantasies). My father best described TR succinctly, “He was a nut.”