How exactly was that touching? Riker deliberately chose not to save the girl and the crew gave him a pat on the back for it. For a series that depicts humanity that's still trying to develop new ways to heal people, the moment when one has the power to bring a dead child back to life is shunned upon. Why is letting this girl die a good thing? Should we go to every hospital and tell doctors to stop trying to revive patients the moment they flat line?
You know what I call characters who willingly let children die and feel good about it at the end? The bad guys.
No one "let" anybody die. As others have already said, the girl was already dead and Riker simply refused to bring her back to life. I agree he probably should have made an exception in this case and revived her anyway (seeing as she had seemingly just died), but you're still crossing a very delicate line when you start bringing back the dead
Riker also had the power to bring back people who died days or years or even centuries ago, but I don't think anybody would argue THAT would be a good idea.