I believe that "kids can be kids" and still learn responsibility. I believe that it is our responsibility as parents to guide our kids and teach them to find a balance between "work" and play.
This means sending them to school and encouraging them to take that Responsibility seriously. Teaching them the importance of getting a good education and helping them do well while still having fun and doing things they enjoy. If they can learn to enjoy school, even better. This also means putting them in charge of caring for their things.
My 2 y/o has a very full and fun life. She has lots of toys and books and movies... We go for walks to the park every day the weather allows, have play dates with other kids, and go fishing as a family. But she knows she has to pick up her toys before bed. And she knows she's going to preschool in the fall (she will be 3) and she can't wait!
Babying your child is not the same thing as "letting them be a child".