Who is Doctor Who For?

I think that sort of criticism is only really valid when it's used as something positive - not "anyone else would be better!" but more "it might be time for something new". Which I agree with! I like Moffat as a person and a writer, but is it time for the next showrunner to get on board? Yeah, of course it is.

I basically start tuning out criticisms when you can't take anything positive from it. Or if someone thinks the only way to fix things is to fire someone specific, be it an actor or a writer. When a critic basically says People Don't Improve So Get Better People, they've lost me.

Well he's on record as saying both that he thought series 9 would be his last and that he was involved in the search for finding his successor, and that they shouldn't pretend it wasn't a problem it was taking so long to replace him, because it was (a problem).

I wouldn't be surprised if he actually wanted to leave after series 8, although I have no evidence for that, just my gut feel. By that time he had done four seasons across five years and two Doctors, very much like RTD.

I seem to be arriving at the conclusion lately that what bothers me about New Who may not have so much to do with who the showrunner is, but rather that the New Series seems to aspire to immortality by being all things to everyone so that all sorts of things get tossed into the stewpot, but I'm not sure if anyone is really stirring it - so there are occasional lumps like The Big Bang or Kill the Moon.

I think the former one could be the best example of the Bigness that seems to sometimes haunt the series (a more recent example being the use of four and a half billion where four and a half thousand probably would have easily sufficed for the purposes of underscoring The Doctor's profound determination). Kill the Moon bothers me because I'm sure I can hear science teachers groaning from here - no one seems to complain much about just pulling completely fabricated science out of your ear in sci-fi of course, but taking questionable liberties with established science is maybe another thing. Nothing wrong with kids being able to counter parental contentions that their favorite show is rotting their minds, with the idea that they might actually be learning something from it. That strikes me as part of the perennial appeal of perhaps historicals especially.

Hence Kill the Moon isn't even allowed near my head canon, yet if the same premise had unfolded a little more sensibly with the moon of an uninhabited planet and had been witnessed mainly from a space station, I think it would probably be a favorite of mine and could have been twice as glorious visually.

Likewise, the new series seems so focused on what are presumably key demographics that I'm almost certain that if we ever get the fabled Talking Cabbage in the New Series, it will undoubtedly be a earth-born, female Talking Cabbage in its early twenties so they can be darned sure that we can all relate to it, but then historically the show will turn around and have completely over-the-top things happen to these companions that perhaps no one can possibly relate to vicariously or otherwise, like Bad Wolf and Clara Splinters. 

I'm not entirely certain these sort of things will be anything that Chibnall can save us from, nor am I at all certain I should blame them all on RTD or Moffat. The roots of Bigness can actually be traced far back in the OS - and to The Key to Time, my favorite DW of all - but I just wish DW had left Bigness behind because it's so hard to keep raising the stakes past "the very fabric of umpteen universes" hanging in the balance.

I'm actually tempted to think that both of the NS showrunners have done a pretty fine job, and I think both of them have probably made a remarkable amount of respectful gestures to the classic series even while trying to take the show to new and interesting places. I think both seem to have a genuine fondness for the series that comes through loud and clear. I've started watching some of the New Series episodes again, and aside from the OTT stuff, so far I've enjoyed each of them even more the second time around and am noticing more of the things that I think that RTD and SM did right.

Sorry, I thought you meant a link for the quote about it being a problem that they couldn't find a replacement and that he wouldn't leave until they did. There are numerous other articles where he stayes that he thought series 9 would be his last. I'll see if I can dig one out, although I am supposed to be working.

This makes very little sense.
No one is forcing him to stay on. Especially, as the next episode will be Christmas 2016, and the next series in 2017. This gap would give the next showrunner plenty of time. Wasn't Xmas 2015 episde filmed in October?
Moffat signed on for series 10 before Hellbents screening.
I really don't understand the thinking behind any of it.

Why change the show if it's popular among the vast majority?

Popularity is an indicator of how much people find something of a good enough quality. Many of us may not like Transformers for instance but the box office shows that to many people they are good films. Personally, I think Doctor Who is a quality show and I don't think it has to make many changes until Chris Chibnall's era.

If the story's crap, the audience won't watch though. That's why independent films generally don't do very well - they strive to break the rules of storytelling and so mainstream audiences tend to find them hard to follow or just generally dislike the move from the traditional Hollywood three-act structure.