I think ultimately, the emphasis on the private nature of all of these social networks has one single limitation issue: the building of network requires few people taking initiative of building the network (which you have identified as "family administrator"). Without such people taking initiative, these networks don't really go anywhere. And we know that not everyone takes those initiatives, especially when the site is brand new, unknown and/or not so popular.
Just some thoughts.
Per your second point, we're extremely grateful to our early adopters who've taken the initiative to try us out with their family. We're constantly working to improve the product from feedback like yours, and trying to lower the barrier so those network builders do take the initiative. Would love to chat if you have any suggestions or concerns about the product!