I did this when I was eleven, for a book called The House of Thirty Cats by Mary Calhoun. I loved cats (and still do). I was astonished when I got a hand-written letter back! That book--and its author--changed my life.
As an adult, I've often found this little exercise frees me up to write better. Maybe it's because I am less concerned with competition when I feel grateful? Or I acknowledge that there's plenty of success out there for all of us?
Thanks to Carolyn See for this exercise. Her book Making a Literary Life is fun and very informative.