This is tl:dr but I've had some thoughts.
Interesting article about how Billie Piper is not going to be the next Doctor despite that appearance and all the mystery and hype around it.
The role is supposedly thought of as a poisoned chalice at this point in time and I wouldn't be suprirsed it that was actually true and not just tabloid speculation balls.
The show is in a horrendous state.
It was going off the boil long before Chibhall came along. Then they tried his soft reboot and the first female Doctor, which was a big miss. Then they got RTD back but it was a completely different writer/person from the RTD who had revived the show almost twenty years prior and he destroyed anything that was left with some of the worst writing ever seen on TV. I don't even think the problem is "woke" storylines, almost any story can be worthwhile if told well... but industry people can't seem to tell stories anymore. It's all about putting the Issue front and centre at the expense of anything else that might make good telly and because the industry has become such an echo chamber where it has become the norm for so-called professionals to get into public fights with the fans on social media, I don't see how things can get better.
Doctor Who has always had a political edge, it was never a problem until the modern era where writers are able to run amok and make everything they work on no more than a vanity project, an ego massage.
I think there's only one way to save Doctor Who specifically and that's along the lines of what Chris Eccleston said in terms of if he'd ever do the role on TV again. You've got to have a complete clear of everyone who has been running it since 2005 but especially Phil Collinson, Jane Tranter, sack Julie Gardener. It's not their show but they've been treated like it is from those at the top. The main reason it's sale is you need to refresh things now and then. Having the same team in charge for 20 years hasn't worked, time for the BBC to admit it.