You know who does it well? The Mormons. When hurricane Katrina hit, the rapid response of Mormons was impressive.
So yes, family, for the most part, is best. Except when it isn't, which happens a lot. Sometimes families could do better, sometimes, it's just not possible, either because of the givers or because of the recipients.
Here's where that sort of rugged individualism comes in: many elders would rather die than have to depend on their kids. They won't tell their kids when they're struggling, they don't want to admit to their increasing frailty and they don't want to be a burden on their families. I know that from experience, from working with elders in my own family, and because I know just how difficult it can be in our society, I already know I don't want to be a burden on my own kids. It's tough, being elderly in our society. We're not a collectivized society, we're an individualistic society, and this is one of the drawbacks.