It occurs to me that once River reaches this point in her timeline, where the Doctor no longer even recognizes her, a big chunk of her List of Reasons to Live is torn away. Sure, here he knows how important she is going to be, but he still doesn’t know her. And from this point on, if she hadn’t sacrificed herself, he still wouldn’t know her. They’re stuck moving in opposite directions, and it would only mean more heartbreak for her if she lived.
Furthermore, I would like to point out that even now, when to him she’s almost as good as a stranger, she never hesitates to give her life in place of his. And in that penultimate gif, that look she gives him, that is pure love. And Alex Kingston is doggon perfect right here because she says the word “spoilers” weighted with all the meaning that it will have, when at this point I don’t think anyone knew how much it says about the Doctor/River relationship without actually saying anything at all.