I always felt similarly about webrings as I did about demoscene. It's less about being strictly practical and more about just a fun little thing you made with your friends. I'd argue that in this day and age, building something from the ground up to be suboptimal by design is a little protest against the quantification and hustle-fication of everything all the time.

Having it be a ring has the nice side effect that anyone closing a ring on your site (or adding your site to it) gets an idea of how everyone in the ring met.

It's more of a fuzzy social thing than a "let's represent social relationships in the most semantically accurate way possible" thing, and for people, I think that knowing how everyone met eachother is a nice thing. You can plan gettogethers off of that. It also keeps people socially accountable; if someone in the group turns out to be a dick, they can just be skipped in the webring.