Yeah, I was always dubious about 10 lambasting Harriet over the whole "kill bad guys" thing- the Doctor has done worse, before and since, to his enemies. Seven arranging for Skaro's destruction via the Hand of Omega? Ten himself imprisoning the Family of Blood forever? Or attempting to rewrite history, declaring himself the Time Lord Triumphant because, well, nobody could stop him?
I think the Doctor is a great character, but part of that is due to his/her/its flaws- left to their own devices, they could easily become worse than The Master and they know it. They'll monologue endlessly about not disrupting the timeline in one episode, and in another, feel perfectly happy upending it (remember how Harriet Jones was supposed to serve three consecutive terms as Prime Minister?) because he was annoyed with how she handled the incident.
I could go on, but the record speaks for itself. We know the Doctor is his greatest enemy (remember the Valeyard?), and we've seen him fight against his tendency to meddle, then dive right back into it, always trying to channel his darker impulses into doing capital-g Good...and while his success rate is probably above 50%, he has some epic failures under his belt, and will continue to do so.
And in my opinion, this is what makes him interesting to watch! It's too easy for us to say "well, he should have acted this way or that"- he's so old nobody (not even himself) is sure about his age, and he's suffering from a host of psychological issues- PTSD, DID, Manic-Depression, OCD, occasional Megalomania- but even at his lowest points, he somehow (usually with some verbal rear-kicking from a Companion) picks himself back up and keeps on trying.
He's simultaneously one of the most human, yet alien characters in fiction. Sometimes hero, sometimes god, most times cosmic hobo. I've been watching the series since I was a young tyke staying up late to watch him on the local PBS station (WTTW Chicago, represent!), and never once have I felt like anyone did a bad job portraying the character or writing for him (though admittedly, some do a better job than others).
I mean, people adore 10 because of David Tennant's natural charisma, but most people forget how many of his stories were absolute rubbish, lol. He was barely even in fan-favorite "Blink". And then you got Kung fu werewolf monks in Victorian England? Or "Love and Monsters"? (Shudder)
The Doctor IS. Nit-pickers and nay-sayers can go to E-Space for all I care.