Why Should Parents Require Unsaved Children to Have Good Behavior?

Here is a summary of an article from John Piper. 

To start, we must be clear that there are no set, defined boundaries for where "child" ends and "adult" begins.  Some things that can be required from younger children should not be required from older ones, but it is the responsibility of the parent to prayerfully discern (usually with godly counsel from those who are in a life stage ahead of you) where on the spectrum their child falls. 

That being said, here are 3 solid reasons to require good behavior from children who have not repented of their sins and are following Christ:

1. It is better for the world (family, friends, church, community, etc) for a child to be kind, respectful, etc.
2. It is good for child to be confronted with the "law" and to have to struggle to obey it.  Why?  It helps him be aware of his powerlessness against sin, and points him to a need for the cross and Gospel.  The child should be frustrated, but all the while being pointed to a Gospel hope, not hopeless exasperation (Colossians 3:21). 
3. If the child does later become a Spirit-led follower of Christ, then all these good character traits become ways of blessing others.  "No parents have the luxury of teaching their child nothing while they wait for his regeneration."