You're absolutely right that all apps have evolved in the same direction, not necessarily because they were inspired by Live Mesh, but mostly because it's a pretty obvious/useful direction.

I think Live Mesh wanted to be the platform piece of that so that (e.g.,) iCloud Photos wouldn't have to implement that themselves. Moreover, it would allow users to have a unified management of the distributed system instead of dealing with each app separately. That's the part I miss.