But what if instead of hosting an index.html file over HTTP(S) we could all host via BitTorrent?
A website could be a bunch of files that are referred to by a DHT hash file.
That way everybody who visits the website will also temporarily support the site by hosting it. If your self hosted site is Slashdotted/HNewsed than hosting would still not fail: after all, all the new visitors are temporarily also seeders of the file over BitTorrent.