You can very much host websites on your machine (not the whole internet, but then again you can’t host the most powerful models either) and you can very much download a Wikipedia or Internet Archive.
But most people never will. This idea that everyone will soon be using local models while frolicking happily in the fields is a pipe dream. Besides, local or not, these models can already be harmful in ways the internet took decades to approach.
A local model works even if the Internet is perfectly firewalled or straight-up down. However, you still need electricity and eventually replacement parts, so in an apocalypse may not work either.
A local model works even if the Internet is perfectly firewalled or straight-up down. However, you still need electricity and eventually replacement parts, so in an apocalypse may not work either.