Nicholas Slayton in The Atlantic:
[P]art of that appeal, not just for viewers but also writers, is its limitlessness. Doctor Who can be anything. If you strip it down to its core concept, it's the platform for every genre and plot imaginable.
“It's a perfect story engine in many ways. The lead can change, you can go anywhere in space and time, the box itself is kind of weird, so we can have an excuse as to why it suddenly disappears at any moment,” said Rudy Jahchan, who along with Liz Shannon Miller hosts the time-travel and Doctor Who-themed podcast Timey Wimey TV. “They can always make it be whatever it needs to be for the years it's in.”
Early on, the show stepped away from its educational nature and started playing with more fantastic ideas, and also genres. There were seasons that played homage to the '60s spy craze, Hammer Horror, and the existential science-fiction stories that filled the '70s. And now the show has fully embraced its genre-busting nature. Recent seasons have mixed pirate adventures, government conspiracy thrillers, and ghost stories, sometimes back to back.
“The appeal of Doctor Who is that you can do anything, any when, you can have him meet anyone,” Handcock said. “That's irresistible as a writer. You're given a completely blank slate, but you're given one of the best characters ever devised in fiction to have an adventure there. You present someone with those two factors, and they're going to leap at it.”
And Doctor Who is uplifting. As dark as the show can get, and as high as the body count can rise (which is very high), there's always a sense of joy and discovery there.