Note that archive.org is not an immutable store, and never has been. Website owners have always been able to ask for pages to be removed, personal data can be removed, and copyright holders can also ask to remove things.
I've had mixed results with that. If I add a robots.txt entry to deny them, they do appear to stop displaying the cached content but then if long after the original content is gone from my site if I also park the domain and forget to maintain the robots.txt entry the cached content starts showing again meaning they never actually got rid of it but rather paused displaying it.
