For what it's worth, I definitely don't organize my tabs in a way where "close to the right" would be helpful in cleaning them up.

I do all the time because the feature exists. I would treat it like a sliding line in my tabs bar. When I'm done with a tab for now it goes to the right, and eventually everything to the right gets closed once I haven't used it in a while

I do. I open a search page, middle click a bunch of links, then want to close all of the ones to the right because I found one that told me what I needed and don't need the rest of them.

It's useful when starting a thread of research of research as new tabs will be opened to the right (Ctrl+Clicking a link). So after it's done, close to the right can be quite useful.