You would be surprised. For one, they can't be bothered to dig anymore. Many of them are mesmerised by aDNA, cropolites (or traces of them in lakes), and whether paleoindians were feminists or gay...
American archaeologists and their desire for fame... Dig up a hole, find the stone tools that evidence human occupation, draw the stratigraphy, do radiocarbon dating, publish in a reputed journal (not your MySpace), rinse and repeat...
Simple. Store everything. I give you an example: the clay tablets written in cuneiform discovered at Ur. They were disposed of by Sumerians, possibly because they have fulfilled their purpose and were simply thrown away. They deal with important things like commercial transactions, but also unimportant things like a personal letter or a poem. This unimportant things pretty much taught all we know about the Sumerian language: syntax, vocabulary, regional variations, etc. In archaeological terms, a refuse is a huge treasure trove, precisely because no one chose what to throw away. Everything is there. It's entirely up to the archaeologist to comb and come up with an interpretation.
> How can enthropy be morally correct or incorrect?
You said the disappearance of content was a feature, not a bug. If it is a feature it was designed. I understood your comment as implying that somebody created this feature.
You now speak about entropy, which one? Boltzmann's or Shanon? This doesn't have to do anything with bit rot or the like. When you write a book, you cannot unwrite it. Is a fait accompli. But if I create a website and I load a bunch of content and after few years I don't pay domain, server space, etc. it will be deleted; at that point a webcrawler may have had copied all the info, or not, we do not know, or somebody may have thought it was worth it and saved a link to it. At a fundamental level, who decides what stays and what is deleted, who owns it if the webcrawler stored it without your permission? These are all moral questions, not technical ones...
Where do you think we have lived the last 5 thousand years? We have clay tablets written in cuneiform that were excavated in Ur from a refuse, and thanks to those we know the little we know about Sumer. The invention of writing made the exercise of forgetting impossible. This has been thoroughly studied by anthropologists like Jack Goody, James Carey, David Oslon, Barry Powell and some other writers like Walter Ong. We live in fact in a terrible world that is mostly trap in the past, where cultural complexity grows in onion layers. Anyone can go back to the past and yearn for it. We can always go back to the past through our stored knowledge, but that past will mean different things to different people as they have not experienced it. Since the invention of the printing press we have lived in a constant state of information inflation. Middle Ages scholars used to complain that with the printing press anyone could read and write books, scholastics were scandalised by the rise in the vernaculars, Michelangelo complained about Flemish painters and their vacuous form of art and so on.
What is worth mentioning here is the rate at which decay is occurring. The articles mentions that 38% of sites that existed in 2013 are no more; that's a decade. How much of that is noise and how much of that is useful information, or at the very least "interesting" content, we don't know. It's gone. How much of that info has been saved by the large web scrappers, or how much is stored by google or twitter is also unknown to us.
What do you define worthy content? A tweet with a million views even though is just an actress semi-naked? A tweet with 300 views about breaking discovery? We celebrated like there was no tomorrow when the internet brought down the gatekeepers, those newspaper, books, magazines, tv and radio editors; just to get swamped in noise, conspiracy theories, memes, tik tok and so on. The problem is that we can't barely cope with the huge amounts of information that is thrown at us and we are too many, with too different tastes to even agree what's worth and what's not.
The "feature" as you've called it, may be by design, but it doesn't mean is useful or morally correct.