Earlier quoted context omitted.
The intent is not to legally bind her, which it obviously wouldn't. Usually the idea of having a child sign too is the idea having a child explicitly agree makes them more likely to be invested in complying. Whether or not there's any evidence that works, I don't know, but it's not quite as stupid as it might seem at first glance.
It is as stupid as it sounds. 4 year old will listen to instructions and if they disobey you take away toys or have silent time, etc. But signing something? That's just really stupid. It's not enforceable and not even understandable.
Many toddlers younger than three could grasp the idea of signing something as a promise to do that thing in the future. A three or four year old could easily understand it.