You would need iCloud Private Relay enabled to encounter the issue. Even then, you don’t get a say in which edge provider you get routed through: it may be Cloudflare, or it may be someone else (e.g., Akamai). It’s up to Apple.
I'm not suggesting anyone should be complaining to you, though--I'm just explaining why some people encounter issues visiting archive.today links and providing them with a workaround (disable iCloud Private Relay).