Huh? You could only access the internet archive using the web too...
Discussion
That's not an os : ) but I get you buy a raspberry pi, find a cheap host then use their app store to find a file hosting soft to host. Man that's a lot we need to reinvent the way hosting operates. It should be much cheaper then what it is now.
Or use a computer you already have. I use copyparty to serve files from a laptop. Could expose over Tor or reverse proxy to cheap VPS.