Like a couple other Vice Presidents in American history, his political party attached him to the presidential ticket as a political dead end where they thought he'd not be able to do any more harm to the party.
There was a somewhat similar situation to this in the Lincoln/Andrew Johnson administration in the 1860's and the William Henry Harrison/ John Tyler administration in the 1840's, so this was not an entirely unknown trick in the political machine tool belt. It was thought throughout the 1800's and early 1900's that being nominated to the Vice Presidency was a complete dead end that a politician could never recover from. It was even still being decided at this time whether it was even completely constitutional for a Vice President to take power after the death of a sitting President. Many constitutionalists at the time thought that a special election should be held during which time, the Vice President simply makes sure the ship of state doesn't sink.
What annoyed the political establishment so much was that TR had fought the New York machine for his entire political career. As police commissioner, he attempted to curb the corruption and bribery that the NYPD which was being used to reward the machine's friends and punish its enemies. Later, as a celebrated author, war hero and anti corruption crusader, he was elected governor of New York and pushed the Republican party even further in trying to end the party machine's influence.
This plan of course backfired when McKinley was shot by a self professed anarchist and TR assumed power. Unlike McKinley, TR didn't just tweak the direction of the United States away from isolation and towards a more robust foreign policy. He truly created trans formative change in domestic policy and redefined the idea of government. None of this would bode well for the old order of the kingmakers that ran both parties, however, in creating the grandfather of Lyndon Johnson's great society, it could be argued that TR merely created a new breed of political elites. But that's a post for another time...
In a sign of how much America has changed since the beginning of the Gilded Age proceeding TR, here's a film clip of his "Shall We Prepare" speech: