River is the Doctor's opposite, his mirror and duality. He would die for the universe, she would sacrifice the universe for him. Yes she does it out of selfishness but love is always selfish, what is marriage if not the ultimate declaration of selfishness 'I want you to be with me forever and nobody else' you might not see the depth because you think River should be a companion/pawn or live a life entirely independent of the Doctor that occasionally entwines with his but River is him in reverse. He had a life then accidentally became a hero out of necessity. She was created to be a killer, to stalk one man, and consciously decided to become a hero instead without changing her main motivation in life, to stalk that man.

And 'River Who'? isn't that just the perfect reason why River is the Doctor's perfect partner, she can steal the show from him