This is the „beauty“ of web rings. Low tech, but brittle if not everyone plays to the rules xD
IIRC they were less "broken" with frames (modulo aesthetic taste) but honestly I don't see the problem with the ring "breaking". Browsers have back buttons; brains do tree search.
If I'm to be an internet reactionary I'd commit to the bit -- underlined blue text to indicate a link, URLs that don't break, active use of the back button and history, etc. =)