The Doctors aren't all that different from one another. Put them in a situation and they'll say the same things. Have them confront evil and they'll want to stop it. Differences in methods, costumes and spunk among them are like shadings; if the actor got the shading wrong - like, for example, Colin Baker, though it turned out it wasn't his fault but the fault of a laidback producer and a script editor who wasn't good at editing scripts - then it feels like the show went way off the rails and the audience recoils. Regardless of who plays the Doctor, it should always feel like this was the same character William Hartnell played, because that's where the show's roots are planted - they've played off that ever since.
And another observation is that they all look like they could be related...if not direct descendants of Hartnell, then distant cousins of eachother. If you can find a black, hispanic or asian actor bearing a passing familial resemblance to those men, or a woman, and if they've got that distinctive spunk or chutzpah to them that reminds one of an outer space alien tourist in a blue box, wielding a vaguely phallic smartphone/flashlight/remote control resembling a vapor pen that it calls a "sonic screwdriver", then....
But then..who is The Doctor? I remember someone wrote on a message board long ago that the Doctor is "...a dodgy geezer in a stolen motor!" So how's that? Too simple? If Joseph Campbell were still alive (read The Power of Myth, it's a very good book, even though it doesn't talk about tricksters, per se, though the Green Knight in Sir Gawain and The Green Knight could count as one, and there's a retelling of that legend in the book), he'd identify the Doctor as the trickster hero of folklore - a character who just might happen to be heroic, but not in a basic, readily identifiable sense. The Coyote. Reynard the Fox. Anansi the spider. Hermes. Prometheus. Br'er Rabbit. Groucho Marx. The Spirit. Top Cat. Snoopy. Bugs Bunny. Among the major comic book superheroes, Spider-Man and The Flash sorta fit those roles, if you could see past their mopey personal lives, but then you also have Deadpool, Loki, Mr. Mxyzptlk, Mister Miracle, Bat-Mite, The Joker and Harley Quin - trickster villains, or trickster anti-heroes, in the case of all but The Joker, who's becoming too dark these days to root for out loud.
Tricksters are also identified as shape shifters. The Doctor's multiple regenerations certainly qualify as shape-shifting. And now the Doctor officially gets to shape-shift in the form of a human female, played by actress Jodie Whittaker, who appeared in Broadchurch, a series created by Chris Chibnall, who is replacing Steven Moffat as showrunner of Doctor Who. Jodie's first appearance was without dialogue in a teaser trailer that showed the Doctor walking through a forest on the way the Tardis, enshrouded in an overcoat and hoodie (the default wardrobe of predecessor Peter Capaldi's 12th Doctor), before stopping short and removing the hood to reveal the new female form..so very like a trickster. In classic folklore & mythology, there are only 3 females solidly identified as tricksters: Lillith, Kitsune and Isis. Isis was the good one...the original Wonder Woman of real-life mythology, who was a 70's Saturday Morning TV superhero, played by Joanna Cameron. Kitsune was a female fox that shapeshifted into human females.
So..where am I going with this? Just that we got a peek at the new Doctor acting the way the Doctor would act in a teaser trailer for a new series/season of Doctor Who. And so far, so good. My honest reaction was that she reminded me of J.K. Rowling with a shorter hairstyle. Obviously, there's going to be moments where her Doctor will reflect on having lived many lifetimes as a male Time Lord, even having been a father and grandfather early in life. But the Doctor as a character has never been distinctly sexual/sexually aggressive, always avuncular..and with Whittaker, perhaps, matronly. It's the companions, however, who sometimes get randy with advances & innuendo (River Song, Rose Tyler, Martha Jones) or became objectified by fans and the show's production team (Leela and Peri). Even though David Tennant and Matt Smith's looked like they could be happy to oblige, the Doctor is not Captain James T. Kirk..or Samantha Jones. The Tardis is not a makeout wagon. Doctor Who sorta leans over the fine line between a family-friendly program and adults-only but never really acted like there was no such line. If the 13th Doctor has a male companion that takes a fancy to her, it's been implied that it wouldn't be the first time a male made advances, but the first time it's happening with the Doctor as a woman. Remember, this is the same character..I imagine there would be a moment where she'd note this distinction, but then move on, because it's always the adventure that's been the Doctor's real romance. Love & marriage are things that are the sizzle, but not the steak.
And the Tardis would have ladies lingerie available, because the Doctor was never adverse to having female companions. Of all the reactions on social media, I thought that was the stupidest, but there were two that were interesting. First is the idea that young boys lose one fictional male role model...well, there are 12 canonical incarnations for them to look at, surely? Unless you're counting future generations...well, that's the power of TV reruns for you. Sherlock Holmes predates several generations of young people. Ditto Indiana Jones and Encyclopedia Brown and Perry Mason and Columbo and Dick Tracy and John Steed and Hercule Poirot and Batman and Superman - all solid male characters created before I was born. And so were Doctors 1-4...and eventually Doctors 5-12, who will still exist for young children to discover.
And the other argument concerns if we'll see an improvement in the stories. Now we're getting somewhere. Doctor Who is more popular than it ever had been, globally, whereas in the past, it was just a pokey cult TV series that wasn't accessible everywhere. Now, it feels like all the stories Steven Moffat wanted to present had been told the way Steven Moffat wanted to present them. It was the same way with his predecessor, Russell T. Davies - fans of the series were getting emotionally exhausted with his spaceships-crashing-into-volcanoes approach to telling Doctor Who stories had run dry..and when he left, nobody was sure if there was anything new to say..not entirely "...on-it's-ass," creatively, but needing a new storytelling style in order to continue.
So...what is Chris Chibnall planning to do? That's the real suspense, here. His early scripts for Doctor Who were middle-of-the-road, journeyman stuff. Proof that he knew what the show was about, but not what it could be under his control...I'm eager to find out.