Password Protected Pages (Parent/Child)

When I create a page (child) and select its parent page that is one that is password protected, shouldn’t this child page be automatically password protected with the same password as the parent unless lets say I create a new password for the child page? At the moment, my child pages don’t make use of my protected parent pages passwords.

This would be an amazingly simple way to password protect and entire area of a wordpress site. On that note: is there a way to password protect the blog itself and not just the underlying pages or posts?