This is an old one which will run & run (I first had a conversation about it with LuluAnn at SotM10). FWIW I agree with @henke54, but the majority historical OSM usage has been cobblestone for setts.
Apart from being more correct :), there is a very useful use case. Setts are a perfectly reasonable surface for older people or other people with balance problems, but cobblestone is very much to be avoided. I would think the same applies to blind & partially sighted people.
I always describe the reasons for my changes in edit comments. In this case, the comment reads
Following that link leads you to the edit which I restored, and from there to the forum discussion that resulted in this edit. (You are linking that discussion in your answer, so I’m assuming you are aware of all this. But I’m mentioning this for the benefit of other readers of this thread because it answers your “why” question: I reverted your change because it contradicts the outcome of that previous discussion.)
Specifically, the outcome of that discussion was that it’s best to use surface=sett for sett roads, surface=unhewn_cobblestone for real cobblestone roads, and accept that surface=cobblestone is de facto being used for both.
The root of the issue is that, quoting from your Wikipedia link, ‘Setts are often idiomatically referred to as “cobbles”’. So your observation that many people tag sett roads as surface=cobblestone is true, but that’s not because of a single image on the wiki – it’s because people confuse these words and everyday usage of “cobblestone” doesn’t necessarily match the dictionary definition. And not just in English either, German has the same problem with the word “Kopfsteinpflaster”, for example.
It’s still worth teaching your fellow mappers about the difference. But because we realistically cannot be sure what people meant when they added surface=cobblestone, the pragmatic solution seems to be that people who care about this distinction use the more unambiguous sett/unhewn_cobblestone values.