For a fine summary of TR's thoughts and options on a possible successor in 1908, see Nathan Miller's biography, Theodore Roosevelt. Tellingly, there's a chapter titled "We Had Better Turn to Taft". In that chapter, Miller notes how Root was TR's first choice--but there were decided problems. First, Root's health was not as good as it might be. Second, and perhaps more disabling, he was identified very closely with Wall Street. That would have made him a tough sell in the western states: not impossible, but definitely not easy. A Root-Bryan election (assuming Bryan would have been the Dems' nominee anyway) would have (IMO) been unnervingly close, but TR's influence probably would have pulled it out for Root.
Another possibility was NY governor Charles Evans Hughes. His policies and credentials were solidly GOP progressive, but he and TR disliked each other, so that was that. Taft was essentially a third choice.
Had the TR/Taft rift not occurred, it might have been possible for the two to come to some sort of off-the-record accord: Taft could say he'd had enough of the presidency after one term and endorse TR; in turn, while making no guarantees (nudge; wink), TR would see what he could do about getting Taft on the Supreme Court. The election of 1912 would really have been about a 2⅓ way election, with Eugene Debs as the ⅓. I don't think it would be a landslide, but I could see TR winning reasonably comfortably: as soon as word got around of Wilson's southern connections/proclivities, that would have been big trouble for him, especially in parts of the US that have monuments to the Union army in public places (e.g., OH, IN, upstate NY).
Then we're in for some very interesting times. Imagine, with his prestige abroad, had TR offered his services to mediate the Austro-Serbian crisis in July 1914...
