The Sandbox was the first feature that Arthur wanted to add to his legacy. Before that, it was perfect as it was, giving him new functions each time he leveled up. He now realized that the new functions were not stored inside the legacy. Jizo created them as he monitored Arthur and his growth.
For example, when Arthur became a lord in Alka, the function was related to Lordship and how to become better. When he became a guild master with members, the party function appeared. Jizo was pushing Arthur forward based on his environment.
This also explained why his legacy gave him runes in a timely manner according to his needs. It wasn't just a machine, but a connection between two people across space and time. If that was the case, how could his legacy even be considered a legacy in the present moment?