But what is "your own server"? Yeah I host my personal site on my raspberry pi, but most people aren't going to do that. They're going to host on a server owned by a company with public stock.
This image could have some smarts to either punch the right holes through the the router's firewall or do something even more clever with a peer-to-peer mesh network.
At the end of the day, what one would have is a website of their own that they control within their residence. It would foster a lot of this small web spirit and be very cheap to bring to market and maintain.