I think a lot of the 'woke' stuff in the specials had more to do with Davies mocking Chibnall. It was , after all, Chibnall who mired the series in a succession of thuddingly woke parables. The obvious boxticking in the Tennant/Tate specials was a bit of finger-flipping from Davies to Chibnall -"You can be woke but still have a fun story" type of thing. You can also be funny without detracting from the mavity of the situation.
My first Doctor was Hartnell - the original and best - rather than Tom Baker (Worst. Doctor. Ever). I had rather hoped that with Peter Capaldi the series would return to presenting the Doctor as an older person. Make them young and attractive and you take away a good chunk of the shows' uniqueness - The Doctor should never be just another action hero, and being an older person was a big part of that. That's why I liked Sylvester McCoy, Patrick Troughton and Jon Pertwee as well as Capaldi and the 'guest Doctors' portrayed by John Hurt and Jo Martin. I'd haved liked to see Brenda (Vera) Blethyn or even Amanda Burton from the original Silent Witness as a female Doctor, and Idris Elba or Lenny Henry as a Black one. Jodie Whittaekr is a skillled actor and Ncuti Gatwa is excellent as the compassionate charmer with a white steel core. But they're both a little young for The Doctor, IMHO. Sadly, Sir Patrick Stewart (a dream choice) is too identified with Jean-Luc Picard. I could see Brian Blessed in the role, though, or for that matter, Stephen Fry!
I'm also still a bit miffed that the Beeb didn't jump on J Michael Straczynskis' expression of interest in being showrunner!