The biggest reason for having Gmail is that it is backed up and accessible anywhere. But this is easily replicated in local caches: You can make it accessible

The biggest reason for having Gmail is that it is backed up and accessible anywhere. But this is easily replicated in local caches: You can make it accessible anywhere with a smart phone. You can back up by encrypting the data with a public key and sending to a drop box type service; with the private key stored offline. Most web apps could be easily replicated by storing the data in an append only structure with timestamps. The internet then just becomes a messaging system. I think the VPN tunnel approach should be pushed by everyone. Lots of companies could secure most of their communication by creating a few tunnels to key clients. Email would be immediately secure without any PKI.