In Jimmy Saville's case, investigating his actions uncovered systematic abuse by many other people. So yes, it should have been investigated, but investigations don't always have to be made public. The focus should be on minimising suffering and preventing further abuse. If the abuser is still alive, then there is no way of protecting the family because it is more important to ensure that the abuser cannot abuse again. But if he or she is dead, then they are no longer a risk to anyone, so there is no need to cause their family suffering.