I'm not trying to advocate for Moffat's writing; I find it tedious, prone to overly emotional appeals, filled with plot holes, and beset with pacing issues. As far as good ideas for series go, each successive series since Matt Smith took over the role has been worse than the last, although I think Death in Heaven was an improvement over The Time of the Doctor. (To be fair, watching my toenails grow would have been preferable to The Time of the Doctor.)
However, I don't find every criticism of Moffat legitimate, for as much as I may agree with many of the commonly brought-up points, others stand out to me like sore thumbs. (As a disclaimer, I should probably say that this isn't directed at anyone.)
So, Doctor Who was rebooted in 2005 with Christopher Eccleston as the Doctor and Russell T. Davies as showrunner. Over the course of that season and all of David Tennant's run, we learn that
- The TARDIS doors are the same on the inside.
- The TARDIS looks vastly different on the inside.
- The Doctor is the last of the Time Lords because the others are all dead.
- The Doctor is fine with having a romantic relationship with a companion.
- The titles no longer feature the Doctor's face.
- John Simm was a totally out-of-character Master.
And no one hated him for it.
We skip ahead to the 50th Anniversary Special, easily one of my favorite episodes of the revival. In it, we learn that Gallifrey's fate is sealed in a parallel universe through the combined efforts of the Doctor's incarnations. The end result is practically the same in that the Doctor cannot get to Gallifrey and does not nullify the Time War as a terrible chapter in the Doctor's personal history.
And a lot of people hated him for it.
So the question is: what gives? Are there enough voices in the fandom willing to criticize Moffat for every decision he makes? Is anything associated with his name tarnished, regardless of whether or not it's problematic?
To some extent, Moffat is subverting decisions that RTD made, especially in the Capaldi era. The 12th Doctor is more aloof and alien, the TARDIS is the most classic design in the revival, the faces are back in the titles, and the Time War has been—as mentioned above—quasi-subverted.
If you dislike his writing because "he's changing the show," you're looking at Doctor Who since 2005. In the scope of its nearly fifty-one years, both RTD and Moffat have made radical changes.
tl;dr Moffat's issues lie more in his execution of concepts than the concepts themselves.