Educational outreach is an important part of what NASA does. For the low cost of a letter they most likely encouraged a kid to have a career in the sciences. In my mind that is peak efficiency.
In fact, probably the only reason NASA still exists is its significant effort at educational outreach - just sticking their head down and working on their projects without communicating with the population that funds them would result in the "NASA does nothing relevant today" meme overshadowing the work it does.