I think it's purely nostalgia from the early days of the web, from before search engines existed. The first webring came out in 1995! Over 30 years ago.

I think there was some sense of creating something to explore, where you didn't get to choose where to go next, there was more serendipity involved due to someone else's curation. No, it doesn't really make sense from a usability or practicality perspective, which is why despite OP, you don't really see them any more.