My inner nerd had a big, fat smile on his face when reading the story and, if I was the person to receive the letter, I'd probably have "wasted" the 10 minutes the response took because I would not be who I am today if not for highly paid scientists encouraging me. And I'd have put in 10 minutes unpaid overtime to make up for it - I'd not be surprised if the respondent did the same.
Kids are import and they really matter for us humans: They'll solve future problems if we invest the time to love and encourage them.
EDIT: Ffs, please unflag the parent comment - do we really only want to read comments that fit into our own bubble? What happened to discourse?
NASA is doing a good thing with promotional actions like this.
Kids need encouragement, they need role models.
Not like that.