10 Totally Different TV Shows that Doctor Who Has Been Over the Years. Almost all by Doctor, but Tom Baker gets two and the Eccleston and Tennant eras are covered in one.
Note that I don't entirely agree, but the show has certainly changed dramatically from Doctor to Doctor and showrunner to showrunner.
I would imagine the educational side doesn't get much play at gaming tables - maybe a solid Celebrity Historical once a season? I hear of teachers using gaming as a stealth educational tool, so maybe it happens here and there.
And the Insane Pantomime probably only happens when the GM isn't paying enough attention - it's certainly an era I haven't delved into, except to pull ideas out of some bottom-of-the-polls stories, shake them off and give them a new lick of paint.
It would be possible to do all ten of these in a single season (these days thirteen episodes, tending to have three two-parters, so ten stories) but what would that look like?
1: An educational adventure show: A straight Historical or adventure based (roughly) on genuine science.
2: A claustrophobic show about monsters attacking: A Base Under Siege. Sorted.
3: An Avengers knock-off: Aliens of London with a particular focus on running around and UNIT appearing and things blowing up. Possibly set in the 80s as played by the 70s. May well involve the Master.
4: Gothic horror movies: This one is not difficult. Choose a monster, put it in an appropriate or deliberately juxtaposing setting, rack up the body count.
5: An absurdist slapstick comedy: Nor is this. Watch City Of Death and take notes.
6: Boys' own adventure stories: Hmm. This is pretty vague. What really makes it stand out is the Doctor's youthfulness. Which is a player option, really.
7: Insane pantomime: Crank up the monster ranting, set it in the 80s or somewhere redolent of the 80s like a tacky theme park or something similarly garish.
8: The Sorcerer's Apprentice: Look at how people, not least companions, view the Time Lord (or equivalent) in your game. Consider their backgrounds, mysteries they might include, issues they could resolve.
9: A postwar survivor's story: War Story.
10: A relationship comedy with universe-shattering consequences: Again, this is a concern for the players. All you can do as GM is complicate matters with varying times and timelines, and possibly NPCs who can stir up trouble as well.