So I have a new head canon regarding Girl in the Fireplace! Kinda. This is after all, Moffat, who adores timeloops and timeline backtracking.
Basically, my new head canon is that at least a part of the Doctor’s melancholy over the letter at the end of the episode is the thought: “Wow … I honestly thought Reinette was smarter than that, having seen into my head and all =("
Could the Doctor have gone back to get Reinette? Why yes, he could have. If it weren’t for her inane letter. (Inane because - why in the name of all that is rational would you send him that letter? Seriously what was she thinking? It’s just a guilt trip, all it says is “come back!" - and why would you need to do that if he DID come back? You wouldn’t. You would only need to do that if he botched it, if he didn’t/couldn’t come back for you - and for someone who’s ‘seen in his head’ and should know about his lonliness, guilt and self-loathing, that’s a guilt trip which is too passive aggressive for words. Lbr, that letter isn’t romantic - it makes no sense unless for whatever reason she was going for a guilt trip, or just plain didn’t care how he felt about it.)
"What difference does the letter make?" you might ask — easy. The letter basically states that he DIDN’T come back for her. He gets a letter saying that he didn’t do something - so he can’t do it anymore (which is the same reason he can’t visit the Brig again - because he was told the extra cup of alcohol was always left untouched). This is the same reason that Rose is stuck coming back to London a year after she left in s1 - because Nine saw the “missing persons" poster saying she’d been missing a year. It’s easily a contributing factor to why alt!Jackie remained dead - alt!Pete and Rose told him she’d died. If Reinette had been a little more wily, perhaps she could have simply stated: “hey, I might not see you again - BUT THANKS FOR ALL THE FUN TRIPS IN THE MEANTIME!" then hellz yeah he could have gone back (the same way he can ‘go back’ to meet Sally Sparrow, or River, or Liz I, or return Cassandra to her original self - despite having met them before - and despite having even watched River die). Or if Reinette had left it vague, he could have gone back (much as he’s able to backtrack and do a shit-ton of redos on Kazran’s timeline, and Amy’s in s5).
This is a concept that is actually remarkably consistent in NuWho - here’s a list of people whose deaths the Doctor witnessed in one form or another, and could therefore not be returned for: in s1, there is Jabe, Gwyneth, the Controller, and Lynda, Based on the fact that he witnessed all these deaths, you could even make a compelling argument that the true paradox (from the Doctor’s perspective) of Pete Tyler’s death/life in Father’s Day was that Nine saw him die alone, and then Rose rewrote the timeline so that he saw Rose run out to save him, and Pete lived instead. In s2, you have Sir Robert, K9, Mrs. Moore, Rickey, alt!Jackie, and Scooti - whose deaths were all witnessed.
How about the people he COULD return for - even if he saw them age and/or die? Easy. They are the people who indicated (or at least left the door open to the possibility) that there had been time loops: Cassandra (in s2), Sally Sparrow, River Song, Kazran, Clara. The beauty of all of this of course is that in most of these cases, the Doctor is relying on them to TELL him about the time loop - with River, he actively seeks this out, comparing diaries. That means that even if it weren’t true, even if it were a total lie and he NEVER returned for them - by telling him that he actually did, they make it so. Kazran doesn’t even want to see Eleven again, and he never tells Eleven he returned — but he never tells Eleven he didn’t!! So .. if you were brilliant, and if you really really really wanted the Doctor to come back for you, all you would have to do is tell him that he had (or leave it vague. Anything but tell him “you never showed up!!" omfgsrsly). He never saw her die, and he never had reason to believe he didn’t go back for her - until her letter told him so. Even Louis left it vaguer than that!!
The worst part of this is that the REAL MdP was a real HBIC smarty-pants, and if she had been in the ep, would never have done that. (Though actually, if the real MdP had been asked to be in the ep, she probs would have said something like "Qu’est-ce que c’est, ce sexist asshat bigotry dans cet episode de OOC merde!! Zut alors, mon roi!!" and would have had Moffat carted off to the guillotine before he could offend her further. That would have been a much better - and more in-character for her - ep, ngl).
As is, the character kinda carved her own fate with that letter.