But, like…take the Doctor out of Moffat’s era and what do you have?
Nothing.
The baddies of each season just wanted to kill the Doctor.
Series 5 had them want him trapped inside the Pandorica, Series 6 had them wanting him to be killed by River, Series 7 just had the baddie running into his time stream to kill him a million times over, and Series 8 was just Missy trying to impress him.
You can’t do that in RTD’s era. In RTD’s era, the Doctor stopped actual evil from killing people.
Lots of people would die if you took RTD’s Doctors out of their stories (shown clearly in Turn Left, too), while nothing would happen to begin with in Moffat’s era if you took his Doctors out of the stories.
Personally, I prefer heroes that are there to save other people, as opposed to being there to save themselves.
I’m honestly not sure if I’m even reading this right (just take the Doctor out of everything and see what happens?), but it’s a fun thought experiment, so let’s see:
Take the Doctor out of Series 5/6/7a: There’s no order of baddies attempting to stop the Doctor, because the Doctor doesn’t exist. Amy grows up with her parents, because the cracks in the universe caused by said baddies didn’t take them away. Probably safe to say she’d still be a imaginative, creative child though. She never gains her deep fear of abandonment, because no-one abandoned her in this ‘verse – not her parents, not the Doctor, no-one. I think she still would have married Rory.
No River, though. Without the Doctor, there’s no River. Or at least not the River we know: maybe Amy and Rory still had a daughter. Or maybe they didn’t. Who knows?
Amy and Rory live long and happy lives but still feel like there’s something they didn’t quite get to have. Travel? Adventure? A sort of vague feeling their various skills were never quite used to their full potential? Amy would feel that most of all. She’s been a storyteller in every ‘verse. Maybe she still writes stories about great and selfish space-wizard heroes, but they probably never get told to anyone but her children.
Uh, anyway (congrats if you read all that) to answer your original question: “take the Doctor out of Moffat’s era and what do you have?” the answer is: Amy. Clara. Rory. Danny. Vastra. Jenny. Cass. Osgood. Kate. Angie. Courtney. Ada. Loads more. All display pretty impressive feats of heroism or cleverness that have nothing to do with the Doctor. (You’ll also notice that in a lot of the episodes I mentioned, the world gets destroyed not because you took the Doctor out, but because you took Clara or Amy out.)
That’s sort of the point of the Doctor though I think? He’s not the hero; the companion is. Sure, he takes Amy to the Starship UK in the distant future and discovers a Star Whale, but she’s the one who actually saves it. I think that’s what Turn Left is about, too – with the Doctor gone, it’s Donna who saves the world, because she had that heroism in her all along and it turns out she had it without even meeting the Doctor. Which is how it should be, really. (Why should her life only start when she meets a man?)
I don’t think the Doctor really is the hero of the show at all. I think the companions are. But I think both RTD-era and Moffat-era make that pretty clear, I really do.