While I think you're correct about how it started, I felt like the change occurred before that point. To me, it started with the end of Martha's tenure. The Doctor on the Titanic and the Doctor meeting up with Donna for the second time were definitely through the Doctor's perspective. This trend continued through the loss of Donna, the specials, and the End of Time.
I think I agree with that assessment. With Donna on as a full-time companion, RTD finally seemed to realize that there didn't need to be a romance angle for the show to work or resonate with an audience. And that while having a "contemporary, relatable character" is a good thing, it's not necessary for that character to be the center of attention.
Having just finished watching "Doomsday" and thus coming to the end of Series Two, I can say with utter conviction it's my least favorite season of the show. "Tooth and Claw," "School Reunion" and "The Girl In the Fireplace" are the only episodes where it actually seems as if the Doctor is more important than Rose. We could argue "The Idiot's Lantern," but honestly, it's Rose that follows the right clues and figures out what's going on, and the Doctor wasn't all that worried about things until Rose got her face eaten off.
The first two series of NuWho are really the story of Rose Tyler, and the Doctor is just the vehicle for her misadventures as much as the TARDIS is for his. It's more of an even split in the first series, and that vibe worked fine, but starting with The Christmas Invasion and carrying through right on up until Doomsday, Billie Piper is the lead and David Tennant is along for the ride. Maybe it took that turn because Billie Piper had a bankable fanbase and David Tennant was hardly a household name at that point.
But ultimately, it's Davies falling into the trap that most writers of modern sci-fi film and television do: thinking that the audience can't understand something otherworldly or relate to it unless we see it through a surrogate's eyes. That notion is complete and total
bullshit, but it's become the rule, the formula, in so much of the genre.
As much as I love Martha Jones as a character, and Freema Agyeman as an actress, the trend very much continues in Series Three. I understand why a lot of people don't like Martha, and can't see her strength; Davies made the horrible mistake of essentially building the character to act as if she was just a "replacement Rose" who failed to win the Doctor's heart. The unrequited crush is an albatross around the character's neck. I can get past it and see the good there, but I understand why many others can't.
Anyhow, tomorrow I'll start with
The Runaway Bride and probably get one or two episodes into Series Three. 13 episodes where I don't have to put up with Blondie the Chav, at least. And Moffat and Cornell's finest hours to look forward to. That'll see me through.