Why didn't the Doctor do anything to fix the oppressive alien society he met in the Doctor Who Christmas special? Because most of the time, the Doctor only tries to preserve the status quo. But occasionally he visits a dystopia where he launches a revolution and smashes the system. Click through for our chart showing the Doctor's waxing and waning revolutionary tendencies over time.
In general, we noticed the Doctor is more likely to overthrow the government on alien planets, or in the distant future. When he visits present-day Earth or our history, he's an arch-conservative. (He ousts Harriet Jones as prime minister of England in "The Christmas Invasion," but that's not the same as destroying the whole government.) Also, the Doctor acted out way more during the Thatcher era than any other period. During the Blair/Gordon Brown eras, he's been quite well-behaved.
Methods: We counted the number of stories in each season where the Doctor overthrows the status quo. (For example, in "The Savages" and "The Happiness Patrol," he encounters a stable society and leads a revolution.) Then we divided that number by the total number of stories in that season, for a percentage. Then we included other events at the time that could explain the Doctor's changing politics.