From the very start, our pupils experience the freedom of playing from memory which is perhaps a skill more necessary for the pianist to develop than for other instrumentalists.
Performing from memory seems to enable more direct communication between the pianist and the audience. Perhaps this is why the convention, now more than 150 years old, still thrives despite its demands.
Children play from memory simply because they can. By the time children have learned a piece, and can play it without difficulty, they will be able to play it from memory. Memorising will never be easier or more natural than for children, and the experience and confidence gained when young is a good basis for developing this ability.