When River dies in the library, giving her life to save the Doctor, the man in front of her mourns the possibility she represents, what he believes she could be for him. But the truth is, he has no idea. The Tenth Doctor is sad, of course, and he would have done everything in his power to save her, but he doesn’t know River. Not yet.
That’s why the goodbye scene in The Name of the Doctor is so important. When the Eleventh Doctor says goodbye to River then, he is mourning their memories. He watched them run. He knows who she is and understands the place she has in his life.
I am not a Doctor/River shipper, but I really enjoyed their kiss in the last episode. River deserved that kiss. She deserved that goodbye, because of all she has been through with the Doctor.
If you hope for River to come back, that is fine. But if she doesn’t, at least know that the last time she appeared she had a beautiful scene and she got her goodbye. And that is beautiful. Sad, but beautiful.
“I’m part-Timelord, part-human…Well isn’t that wizard.”