Facebook is not for intimate conversation with your family. Path is mobile-first and isn't as big of a thing (yet). Google+ allows you define circles but is rather complicated. As with other spaces where network effects are important, only the biggest will survive and the biggest currently (Path/Google+/others) do not address the family niche conclusively (product wise/platorm wise).
The real question is whether the family niche itself is an important enough one to a large enough base of people. It makes more sense to assume that this is the case...than not right? The upside here is pretty huge if there's something to it.