I’ve got some further thoughts on the subject (deep or otherwise), but I’ll post them as main entries after I’ve had a chance to edit them for a while.

Some thoughts, not to dispute your argument, but just (perhaps as Devil’s advocate) to maybe challenge one or two points:

There were always two or three companions (iirc) before Pertwee, and that didn’t stop there being some great stories. They were multi-threaded, with the companions splitting off and becoming involved in different subplots, and it worked well, and didn’t diminish the Doctor.
During Pertwee and most of Baker there was one companion. That worked great too.
In the new series, there has been one main companion, with other “minor” companions joining for a few episodes. This has been an excellent device: Captain Jack’s arrival in the Tardis after Father’s Day enabled a complete change of dynamic when the everything interesting in the Doctor-Rose relationship (“just another stupid ape!”) had been done and before it became boring.
Some of the more memorable companions have enjoyed a slightly abrasive relationship with the Doctor. Leela, Romana and Ace have disapproved of, or been disapproved of by, the Doctor. For me, this makes for an interesting relationship, in the way John Steed’s relationship with Cathy Gale was more interesting than that with Tara King because Mrs Gale not only disapproved of some of the decisions and choices he made but because she disapproved of his vocation and his lifestyle (while Tara spent her time gazing at him adoringly). Interesting Who stories often involve a moral dilemma: the classic example is in Genesis where the Doctor questions whether his means justify the end. It’s great when the companion and the Doctor can disagree.
The better companions have had a more mature relationship with the Doctor. Just as you knew both Steed and Mrs Gale would lay down their own life for one another, you understand that ultimately the differences the Doctor had with those companions didn’t matter. The problem with Teagan, say, or Peri, was the differences manifested themselves in bickering. But with, for example, the Doctor and Leela, you can see them question their own convictions; the Doctor sometimes seems almost to turn a blind eye to Leela’s blood-thirst if it suits him: a fascinatingly flawed moral position!
The constraints of the new series format has perhaps imposed a necessary discipline on the writing and the editing. We’ve certainly had some great one-offs (The Unquiet Dead and Tooth and Claw for example) although I will admit I have felt many stories were rushed, and would like to see more multi-parters. All the same, I feel the old format encouraged padding and laziness, and whilst all Who fans love cliffhangers, for every “You will perish under maximum deletion” there is too often an Age of Steel let-down to follow.
The quality of the writing during the ’60s and ’70s was, generally, higher than during the ’80s.
The problem with some of the Davison and Baker serials was a sense that you needed to tick all these boxes for a serial to be exciting. You had to cram it all in, because the quality of the writing was such that it could not stand by that alone.
Although I’ve commented after your reviews of Resurrection, Revalation and Fenric that the stories have too much going on, I don’t mean I don’t like complex stories.L
Stories need to be cohesive; to take Fenric as an example, some of the subplots worked: because we had codebreaking, the Enigma machine, deciphering the runes and Ace deconstructing her fears were all part of the same story, in the way that a time-travelling manipulative wolf wasn’t, quite.
For me, The Girl in the Fireplace is the perfect example of a well structured, multi-threaded multi-companion story told within the constraints of a 45 minute episode. But then, as you say, Steven Moffat is a brillliant writer, in the way that Eric Saward, say, is not.

I’ll leave my reasons why The Avengers deserves to be at the top of that list of greatest ever TV series for another time.

Some thoughts, not to dispute your argument, but just (perhaps as Devil’s advocate) to maybe challenge one or two points:

There were always two or three companions (iirc) before Pertwee, and that didn’t stop there being some great stories. They were multi-threaded, with the companions splitting off and becoming involved in different subplots, and it worked well, and didn’t diminish the Doctor.
During Pertwee and most of Baker there was one companion. That worked great too.
In the new series, there has been one main companion, with other “minor” companions joining for a few episodes. This has been an excellent device: Captain Jack’s arrival in the Tardis after Father’s Day enabled a complete change of dynamic when the everything interesting in the Doctor-Rose relationship (“just another stupid ape!”) had been done and before it became boring.
Some of the more memorable companions have enjoyed a slightly abrasive relationship with the Doctor. Leela, Romana and Ace have disapproved of, or been disapproved of by, the Doctor. For me, this makes for an interesting relationship, in the way John Steed’s relationship with Cathy Gale was more interesting than that with Tara King because Mrs Gale not only disapproved of some of the decisions and choices he made but because she disapproved of his vocation and his lifestyle (while Tara spent her time gazing at him adoringly). Interesting Who stories often involve a moral dilemma: the classic example is in Genesis where the Doctor questions whether his means justify the end. It’s great when the companion and the Doctor can disagree.
The better companions have had a more mature relationship with the Doctor. Just as you knew both Steed and Mrs Gale would lay down their own life for one another, you understand that ultimately the differences the Doctor had with those companions didn’t matter. The problem with Teagan, say, or Peri, was the differences manifested themselves in bickering. But with, for example, the Doctor and Leela, you can see them question their own convictions; the Doctor sometimes seems almost to turn a blind eye to Leela’s blood-thirst if it suits him: a fascinatingly flawed moral position!
The constraints of the new series format has perhaps imposed a necessary discipline on the writing and the editing. We’ve certainly had some great one-offs (The Unquiet Dead and Tooth and Claw for example) although I will admit I have felt many stories were rushed, and would like to see more multi-parters. All the same, I feel the old format encouraged padding and laziness, and whilst all Who fans love cliffhangers, for every “You will perish under maximum deletion” there is too often an Age of Steel let-down to follow.
The quality of the writing during the ’60s and ’70s was, generally, higher than during the ’80s.
The problem with some of the Davison and Baker serials was a sense that you needed to tick all these boxes for a serial to be exciting. You had to cram it all in, because the quality of the writing was such that it could not stand by that alone.
Although I’ve commented after your reviews of Resurrection, Revalation and Fenric that the stories have too much going on, I don’t mean I don’t like complex stories.L
Stories need to be cohesive; to take Fenric as an example, some of the subplots worked: because we had codebreaking, the Enigma machine, deciphering the runes and Ace deconstructing her fears were all part of the same story, in the way that a time-travelling manipulative wolf wasn’t, quite.
For me, The Girl in the Fireplace is the perfect example of a well structured, multi-threaded multi-companion story told within the constraints of a 45 minute episode. But then, as you say, Steven Moffat is a brillliant writer, in the way that Eric Saward, say, is not.

I’ll leave my reasons why The Avengers deserves to be at the top of that list of greatest ever TV series for another time.