I've become interested in evolutionary psychology. Not at all expert, but when one considers the survivability of children in ancient (pre-historic) environments, seems logical that children increased the likelihood of survival by mimicking the adults they see; figuring out how to do the basics like feeding themselves, finding a safe place to sleep, taking cover during inclement weather, and generally assimilating adult behavior. The sooner they learned these skills, the better their chance of survival if they became separated from adults. Evolution selected for such behaviors.
That conclusion is a thought experiment, and I haven't dug up scientific evidence, so an anecdote: I once came home from work to find my 6 year old daughter in my closet. She had put on one of my shirts, a tie and my shoes. She was holding an old briefcase. When she saw me, she said, "daddy, let's go do some business!". I believe that kids have a genetically driven need to emulate their parents and that need is rooted in evolution and is much more profound than we realize. Regrettably, the modern parenting and schooling systems squelch that need.
Here's another anecdote: http://www.newyorker.com/arts/critics/books/2012/07/02/12070...