This is slightly recycled material for this blog, but this is discourse from a recent Doctor Who thread that discussed "Series Two" (David Tennant's first season). Spoilers, of course...
I'm not arguing that it isn't a love story, as obviously it is, but it is interesting that given that element as the prevailing arc for this series, the episode that had Tennant's doctor at his most lovesick was the brilliant "The Girl In The Fireplace," and that wasn't Rose that he was mooning over. The chemistry between Tennant's Doctor and Sophia Myles' Madame de Pompadour buries anything we ever saw between the Doctor and Rose in my opinion. Perhaps it's no surprise that Tennant and Myles became a real-life item. (The other great thing about that episode is that Rose appears to be wearing a Wichita Falls t-shirt throughout - for what reason, I can't imagine.)
One other Series 2 comment: I've seen every episode of Doctor Who that the BBC did not misplace, and I'm much more of a Moffat guy than a Davies guy, but - even with those provisos - that moment of trash-talking between Daleks and Cybermen in the Series 2 finale "Doomsday" might be the most fun scene in the show's history.
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Perhaps I was a little harsh in that assessment, as in the end I did find the interaction between Rose and The Doctor to be emotionally stirring - both at the end of "Doomsday" and in reference to the spoilers discussed by others above.
I guess I am one of those people who - after all those years of very platonic adventures from Doctors 1 - 7 - does find the whole premise a little difficult to accept. It's not that it wasn't executed competently; it's more that it runs contrary to what we had seen before (with the exception of course of the very regrettable TV-movie).
With the destruction of Gallifrey, though, I acknowledge it's not out of the question. He has reason to be much lonelier than he was in his earlier incarnations, and Earth is his favorite planet, so it's reasonable that he could fall for an Earthling. It's just that he's so much more worldly (or "universally," if you will) than any Earthling could ever be, so my brain tends to put The Doctor on a separate plane from his companions.
Perhaps a lot of this stems from a broader problem I have with the new program (all four years of it), and that's that the thing is just so Earth-bound. I know there were cheap sets back in the day, way too many humanoid "aliens," and some rubber suits that many would find laughable today, but I loved that the Doctor did much more traveling to different planets and interacting with different alien societies. I haven't done a count, and I know they're on a budget, but one of the things that threw me off most about Series One was that we just kept coming back to Earth to hang out with Jackie, Mickey, etc. And then we have continued with that sort of thing, barely branching out to the interiors of spacecrafts, the Moon, and "New Earth." Most of the adventures take place on Earth or concern the fate of Earth. They've managed to keep it interesting on a storytelling level for the most part and have established good characterization, but I'd love to see more intergalactic imagination injected into the show more frequently.
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That's a good point about MdP, and I did feel as if Rose had a lot of catching up to do to be at The Doctor's emotional "level." You articulated that well.
The various Doctors have always had an irrepressible youth and wonder to their spirits - Tennant especially so - but I suppose there comes a point at which I wonder about the romantic compatibility of someone centuries old with someone who is not. I realize MdP would also not be centuries old; this is just more of a general statement on the inclusion of romantic relationships for The Doctor with his companions. But who knows? I also bought the relationship alluded to in season four with Alex Kingston's River Song.