I believe that our kids don't know their own motivations all the time either. It's our job as parents to help guide our children to uncover their motivations and understand their behaviors over time. One of the things I love about the division of responsibility is that it provides a model for allowing some of that learning to take place. Children need the opportunity to learn their bodies ~ to learn what it feels like to be full and hungry. They won't learn as well if they are frequently told how much to eat. Will they make mistakes sometimes? Absolutely. It's part of the learning process.
TwinToddlersDad points out accurately that parents fear leaving their children hungry. Parents also have fears that their children haven't eaten enough, that they won't grow adequately, that their health will be affected, that they make wake up in the middle of the night hungry, and many other food- and eating-related fears. I would guess that these fears are based on instinct and human survival. But in most cases, we can take a step back and make a realistic assessment. Most (but unfortunately not all) Americans have adequate access to food. Most children (but again, unfortunately not all) do not have significant nutritional deficits or growth disorders. So most parents realistically do not need to let these fears guide their parenting decisions. If our generally well-fed, typically growing, healthy child goes to bed hungry one night, what's the worst that can happen?
There is also a risk in not letting it happen. By not giving our children the opportunity to learn whether they are full or not without our interference, we can be putting them at risk for poor management of their eating and weight as they get older. Our nation's growing obesity epidemic is likely influenced by poor body awareness and food regulation skills.
I know from personal experience that it can be difficult to put aside those fears and worries about related to our children's eating. But I encourage you to try. Reframe those worries into opportunities for learning and growth and see what happens over time.