mainframe -> minicomputer -> PC -> smartphone

Yes, git would be great for these kind of tasks if it could do fast automatic replication. I've tried to move our scientists to git, but they resist. Indeed, DropBox works just fine for them - they don't need to do explicit commits, pushes and pulls. You just change a file and it's changed on the server.

Oh, and they're using rsnapshot for backups. So git's ability to store history is not really a selling point.

>that is vastly different from the network filesystem approach where the application and user treat the remote storage like it was local storage
As I see it, there are several main reasons for remote storage:
1) To be able to access large storage. It's not really a problem now when a typical notebook has more space than a SAN 20 years ago.
2) To share something. Dropbox works just fine for it in most cases when you don't need locking and sub-millisecond coherency.
3) To access archived data.

So DropBox works great for a lot of people simply because it doesn't try to do everything.