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.
The trouble is that most people who have it enabled don't realize. If you're paying for iCloud+, it's likely enabled.
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).
Anyway, for what it's worth it works fine on my iPhone using iOS Safari.