This is where I think that you're smarter than the current average Doctor Who fan.
I've long said that one of my problems with modern Who is the focus on The Doctor's love life, which was none more evidenced than by the Nine-Ten/Rose love story, followed up later by Eleven/River. I think a lot of people lost interest in Capaldi - writers included - because he wasn't fuckable enough for fangirls.
If you can envision a better canon for Doctor Who than who The Doctor is available to fuck, it might just be because you have a better sense of intellectual curiosity than the typical fans do.
Pretty much this. The Doctor is largely asexual. Probably because Time Lords are
extremely long lived so they need to be and because they're mentally so advanced that flirting for them is probably a years long process.
Only on a couple of occasions have I entertained the idea of the Doctor being romantically involved with a companion. And it certainly wasn't with Rose and it wasn't with River Song either. The latter in theory had the right set-up for a romantic interest in that she was
supposedly equally intelligent and compatible. But it fell flat because she never once came across as equally intelligent and the actress had all the sex appeal of a plank of wood so the audience (at least this audience) couldn't really get on board with the idea.
Romana I had chemistry with Tom Baker. There was a subtle undercurrent that felt like Time Lord flirting and of course Mary Tamm was more than easy on the eyes. Plus they're both the same species. I feel that helps. The only other time I can think of (and here come the downvotes) is Clara and Eleven. They had chemistry, she was one of the smarter companions and the character had an emotional guard-rail that suggested she'd be able to be involved and then when the inevitable happened due to either age or Dalek, she wouldn't go all Amy Pond or Martha Jones about it. There was an easy familiarity between Eleven and Clara that really worked. They were completely comfortable with each other. Whereas the relationship between Nine and Rose was like... a rich old guy and his spoiled bratty arm-candy. It was all about entertaining her, protecting her, the works. And Martha, well honestly Martha deserved better than arbitrarily being paired off with Mickey in a post-story wrap up montage. She was intelligent, a doctor, ambitious. He was the tin dog.
Of course I know I'll get disagreement because they really fucked up the story and canon starting around the time of Clara, because the idea of the Doctor never being romantically involved at all is sacrosanct for some (the granddaughter came from somewhere, though!) and there was that dreadful way they packaged off Clara with the tiny viking woman (with whom she had no chemistry at all, unsurprisingly). Or that entirely forgettable guy from the school who she had almost less with.
But Jenna Louise-Coleman had the looks and the personality in buckets to get me on board with it and right from The Snowmen they were sparking off each other in a very entertaining way. So in nearly 900 episodes classic and new, Lord knows how many companions and guest stars, those are the TWO characters I think it would have worked to have romantic involvement with. And quite possibly did in canon but off screen because it's not that sort of show.
And before you reach for your keyboard to disagree with me, consider for a moment the anguished howls from all the Rose-shippers there would have been and tell me it wouldn't be music.