Right, I only mentioned Dewey to illustrate my point since it's likely the best known. Of course there are many others such as Universal, Library of Congress, etc., etc. I'm not saying that any of these are suitable for the site I'm suggesting, perhaps we need to pinch the best ideas from each and tailor a new version specifically for the web.
What I will say is that taxonomy and classification systems in general are problematic and have always been so. Anyone who has ever tried to sort and classify stuff knows this! I'm forever sorting the myriad of stuff on my PCs, smartphones, etc. into various classifications and then into appropriately named directories and it's an ongoing struggle.
If I dream up too few classifications then I end up with directories that don't have sufficiently specific names to find things, too many and I'll lose items in directories whose names that are a near match but not sufficiently so. If I ignore the obvious catalog/directory naming system and use a program such as Everything that finds stuff anywhere based on name then I'll lose the ability to browse (grouped) like subjects as their names won't necessarily be sufficiently alike. It's all a damn nuisance really.
Then there's the problem of what you classify by: subject, or author's name or physical object (a major problem in a general purpose catalog).
I could write an essay about nomenclature and how it's a significant problem for the web and IT generally. For instance, if people were a little more knowledgeable about taxonomy and classification in general - and that includes both general web users and website owners - then Google could be spared millions in electricity costs due to much more accurate search results first time around.
That said, existing classification systems have their uses even in days where electronic sorting has come into its own. Take a
physical book library for instance, I'll check out some subject in the catalog index then go to the book in question - and, as more often than not, I'll browse many of the nearby books on the same subject. The fact that they're grouped together by subject is very useful. If they were grouped alphabetically then this would not be possible.
I take your point that in practice the public's constant need for links, discussion etc. However, I don't see this as inconsistent with what I've suggested, especially so if one doesn't take a one-system-fits-all approach as is so often the case not only on the web but with software in general.
For instance, with Windows 8 when Microsoft moved away from the traditional IBM/CUA-like GUI to its new Metro GUI, it didn't allow users a choice to retain the old GUI. This programmer-know-best arrogrance permeates both software and the web like a bad smell and it does nobody any good.
I see no reason why the site I'm suggesting can't have multiple methods of access. The Dewey-type, search a la Everything, and also those along the lines you've suggested. Moreover, there's no reason it cannot have user comments in the same way Hacker News does.
The key to its success would be in having wide appeal - by providing both casual and sophisticated users a service suitable for each. As the saying goes, to each according to his/her needs.