The savings are managed by the person themselves, to speed up the growth of their sense of independence and self-management.
When I turned 7, I also intended to work in town for the orphanage and my future, but I was stopped by Elle-sensei.
I had already contributed lots of money from reversi and other toys.
If on top of that I were to work it's possible that the other kids will lose motivation, thinking "wouldn't it be fine if we don't work and earn money as well"