The idea is interesting and even kind of tech-funny.
But man, you really have to explain how it works a bit better. At first I thought that we should redirect 404s to your website and I was: "??".
What I understood: Which each iteration of the website, you archive the old one on a specific subdomain. Then, you redirect all 404s of the new website to the old one. Like that: no link is broken.
Agreed, I thought this is a service that would provide automatic redirects to the Archive or similar.
FWIW Brave does that. If you reach a page with a 404 a banner will appear on top with a button to try and navigate to the latest version of the page you're looking for at the archive.
There's a fantastic extension for Firefox, Chrome, etc. called Web Archives which will attempt to find a copy of the missing page from the Wayback Machine, Google Cache, Archive.is and many more.