Very likely true that there were older teenagers in orphanages, but in the case of the musical, Annie, the roles were not written for older teenagers.
A little off-topic but related due to age, I am interested in following 13 on Broadway, especially because of the ages of the cast members. I didn't see the Connecticut production, but I think I said before that I don't feel adults will be the show's big draw. That might be okay because have you ever seen the hordes of teen drama groups in the city??