Directory sites and webrings were artifacts of the early web, when search engines were pretty bad. They disappeared once search got better.
After that, sites also stop linking to each other.
Sure search engines got better, and then they got worse..
Many of the things 'web rings' promoted were 'similar sites'.
Yet it was when google become big that it destroyed web rings and blog rolls (which were similar to web rings, but often included a variety of sites not just similars) -
It became known that google penalized people for linking to other sites, linking to 'bad neighborhoods' - they would sometimes call out sites publicly for giving 'link juice' to others for profit..
Web rings disappeared and blog rolls as well, because google.
Not because search engines got better, but because google threatened to penalize you for linking out.
It feels like at some point in the last 5 years we crossed some threshold where search engines are so optimized to the commercial space and selling junk that obscure searches yield no useful information. Any keyword which is so unfortunate to overlap in the commercial product space will just dominate your results and make them mostly useless. Even my advanced google fu to tack on certain phrases and other bits of language to narrow things down and formerly gave very focused results but now feels like google is atrophying in that domain.
It doesn't help that our culture has become so word overload friendly where instead of creating new words and phonetic combinations existing words are used instead and now require disambiguation to say not the product kind of this word.