Well, full text search is really power hungry. Once you have few gigs of email, your phone's local full text engine is going to get too slow. This is a good reason to keep email on the remote server.
That said, your personal communication will be stored on the servers encrypted if you use encrypted chat like Whatsapp or Telegram.
I am not sure why you had to use cloud server when sending files over LAN. I've uploaded videos directly to iOS over ftp server, and Android has tons of apps to sync data back and forth, all locally.
I am not sure why your TODO list needs a central server -- Simplenote does not require login, and it totally happy to keep everything locally. There are integrated note apps as well.
So to summarize: everything is there already. But people prefer to choose a simple solution and use cloud-based service, instead of doing a little bit of work and creating "machines which can function as islands"