maybe there's a light that's always on

Yes, yes, yes, to everything you just said. The Doctor has such major guilt issues about things he can't even really be held responsible for - something like this is just bound to leave him all torn up inside and pretty full of self-loathing. And at least from my view of the character, he's pretty full of repressed self-loathing anyway.

I'm glad you enjoyed the story, and thank you very much for the lovely comment.