It's not impossible that if TR had pointed to Root and Root were the nominee, he (Root) might have lost a real squeaker to Bryan--and I mean one wherein the winner wasn't known until perhaps the Friday or Saturday after the election. But then, I'd bet Bryan would be a single term president. As naive and inexperienced as he was, it's all but impossible to imagine him as an effective chief executive (think Harding without the corrupt friends and also without advisors like Hughes and Hoover). That paves the way very neatly for TR's return in 1912--at the head of a united GOP, I might add. In this situation, TR would have no difficulty in beating Bryan.
I suggest that it also means the phrase "President Woodrow Wilson" would be strictly a creature of alternate history. IOTL, Wilson pretty much had one shot--1912. If he hadn't gotten the nomination then, by 1916 he'd have been out of elective office for three years and could well have been forgotten.