It seems to me like one could market a device that isn't much more than a RPI that would download a container image from small-web-dot-registry that would run a webserver that encapsulates the site one authored on small-web-dot-com.

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.