I get this request a lot actually. The reason I decided to not do it was because webrings, though nice, had a lot of problems. The main issue was that people's sites would go away, and then the ring would break. I also didn't want to introduce any functionality that would make sites depend on Neocities backend APIs to function. Web sites are more long-term and durable if they remain (mostly) static.
I tried using "tags" that could bind sites together on Neocities, but to be honest the idea has largely been a failure. People will tag their site "anime" and their site will have nothing to do with anime... but it's a popular tag so they add it in just so they're on a popular tag. Geocities had this problem to a certain extent too (a tech site being in the non-tech neighborhood). You can get a flavor of the problem here: https://neocities.org/browse?tag=anime
One idea I'm considering is to only allow a site to have one tag, rather than 3 like I do right now. Maybe that will stop people from adding tags that are irrelevant to the content of their site. Or it may compound this problem. I'm on the fence about it.
Another idea I'm considering is allowing people to create curated lists of their favorite sites on Neocities, similar to playlists on Youtube. The "follow site" functionality kindof does this, but in a generic way, and it tends to be a bit... I guess nepotistic (hey you're popular, follow me so my site can get more popular too!)
I'm always happy to hear ideas on how to improve this. I do like the idea of related sites being able to clump together, but in practice it doesn't work as well as I would like it to. But maybe it works well enough and I'm overthinking it.
I've got a fancy 1080Ti and Tensorflow. If you have any particular things I could try or should read about, I'm happy to look into doing some research! Googling for "Tensorflow recommender" gave some interesting starting points.
No, I get this request quite a bit from people that sincerely miss web rings. I'm not sure how much of it is anachronistic nostalgia and how much of it is a true desire to bring it back. To give an example of this, I've gotten more than a few requests to add the Gopher protocol to Neocities.
IIRC the old webrings had a CGI backend that would collect the addresses and then you would click "next" and it would take you to the next site. But yeah you could just make a vanilla one. You could also just make one outside of the context of Neocities.
But if the next site went down or didn't link to the next site correctly, you couldn't proceed. That was always my problem with webrings. They depended on each site to embed the ring code properly, and usually they didn't, so you were stuck trying to find a working one. It was a pretty lousy UX overall.
It may have been lousy UX, but I suppose it also provided a social convention of not breaking the chain. Weakest links and all that. Relevant to the OP about linkrot!
Maybe a modern equivalent would redirect downed sites to the IPFS archive.
That's interesting the ones I remember were literally rings of static links, coordinated by the webmasters, presumably over email. I see what you mean now.