Adults, not children, deserve total privacy. Giving a child total privacy simply welcomes in bad situations and problems. Parents need to actively monitor their children to a slight degree without being overly intrusive. Being overly intrusive comes with its own consequences, so parents need to tread carefully when it comes to their child's privacy.
No, children should not have total privacy for safety reasons. A child does has a reasonable expectation to limited privacy, but not total. A parent should be able to know what a child is generally doing with their time, as a child does not yet have the mental capacity to accurately assess dangers.