> imagine an Internet where the data about each user (what would normally be entries in different tables on the servers) is stored, encrypted and authenticated, on the user's computer, as opposed to being stored on the server.

Trying to authenticate solely on the client side isn't as fruitful as you might be imagining, since it introduces potential security isues. Without any server-side authentication using only information (i.e. a blob) that the server has access to, it becomes very easy for clients to spoof/pretend to be other clients.

Consider that if this kind of system were easy/fruitful to implement, a lot of businesses would have done it already to avoid increased development/server costs on their end.