I would like Jodie to stay on under a different producer, just because we haven't seen that yet in Modern Who, and because I'm extremely not a fan of Chibnall's style. Were that I knew who should take over, though. I think part of the issue with this era that the RTD-to-Moffat transition escaped was that it was pretty obvious for a long time that Moffat would be the ideal successor to RTD; he had experience running TV shows, and his episodes each year were always highly-praised and well-liked (I feel like people were anticipating Moffat as the heir-apparent after, like, "The Girl in the Fireplace"). There wasn't a similar all-star writer during the Moffat-era.
Agreed. Chibnall was at a distinct disadvantage that way. Honestly, if they wanted to pick a good writer from the Moffat era, I would have gone with Toby Whithouse. I think he had a pretty solid collection of episodes on his resume-- "The Vampires of Venice," "The God Complex," "A Town Called Mercy," "Under the Lake," "Before the Flood," "The Lie of the Land." Nothing as flashy as Moffat's early episodes but solid executions of the
Doctor Who formula.
IIRC, they did offer the showrunner position to Whithouse but he turned it down. I don't think that the BBC offers enough money for most people to put up with all of the aggravation that comes with being
Doctor Who showrunner. If they're not willing to open their pocketbook and pay one guy enough to make it worth their while, then maybe they need to start poaching writers from Big Finish and pair them up with seasoned producers to handle the nuts & bolts of TV production.
I don't know that I want Whittaker or Chibnall to leave right now. I wouldn't mind seeing Whittaker under a different producer to see if she can up her game by showing us a different side to her Doctor. But the stuff with the Division & the Timeless Child are dangling threads that I would rather see Chibnall resolve if he can. The biggest problem is the show losing its sense of fun. The show had an energetic family appeal during the RTD & Moffat eras. If Chibnall could just give us a few more sprinkles of "Dinosaurs on a Spaceship" each episode, I think it would go a long way towards improving the series.
The people saying that it needs a rest are totally missing the obvious. The 2 lowest rated seasons were the ones that came immediately after a 1 year hiatus. That's what's damaging the show's ratings. Take it away for long enough and people get out of the habit of watching it. Even if you can't manage a full 10 episodes per year (which seems pretty pathetic if you can't since RTD did 14 episodes per year for 4 years straight, not even counting the spinoffs), you need to do a special every 4-6 months to keep the show present in people's minds.
You already have two of your campions leaving so that might open the door up for Captain Jack as a regular or something like that.
I don't know that I'd like Jack as a regular at this point but they may need to do something drastic like that to get the lapsed fans back.
One thing's for certain - the complaint of "too many companions" doesn't hold up when shows like "Sliders" made having ensembles of four work.
The number of cast members is dependent on making sure that you properly balance them with each other. The only time that 3 companions worked was during the early Hartnell years with Ian, Barbara, & Susan/Vicky. And it worked because they were properly balanced. Ian & Barbara had a strong relationship with each other and Susan/Vicky was the kid who got in trouble and got captured. Other instances of 3 companions didn't work. Ben/Polly/Jamie didn't work because Ben & Jamie were both rough & tumble action guys, so there was no need for both of them. Adric/Nyssa/Tegan didn't work because Adric & Nyssa were both quiet science nerds.
Similarly, is there any reason why we need both Ryan & Yaz? Couldn't they have been rolled together into a single character? Also, because we were also starting with a new Doctor, it meant that she got less development because there were so many companions to establish at the same time. And it's even more of a missed opportunity because, although they were different people, they all came from the same place, which limited how different their perspectives could be. I think maybe what they should have done was just started Season 11 with Graham & Ryan and then added Yaz halfway through in "Demons of the Punjab" but had her actually be a woman from 1947 India. It scratches my desire for companions who are (1) not from the present, (2) not from the U.K., and (3) added mid-season to make it feel like middle season episodes can have actual consequences to the regular status quo.
It would like saying Lex Luthor was really a Kryptonian all along. Or that Krypton never exploded. Might make an interesting alternate story, but not in the main continuity.
I see what you did there.

As flawed as
Superman Returns &
Man of Steel are, we definitely dodged a bullet by not getting the J.J. Abrams script.