I'd posit, precisely, that it isn't eternity. But a putative eternity or an "implied" eternity ...
... but nowhere near that in actual practice, to the point of being potentially ephemeral, to our detriment.-
(Naught of which subtracts from your valid concerns, where warranted ...)
While we speak of "eternal" digital footprints, the actual lifespan of this data is dictated by evolving technology, legal changes, and human intervention. This illusion of permanence can lead to a false sense of security or unnecessary paranoia. Recognizing the difference between theoretical possibilities and practical realities is crucial. The concept of "eternal" digital storage is far more ephemeral than it appears, and this impermanence could pose both risks and reassurances.-
Panopticons and surveillance are different matters.-
Anyway, none of the civilizations in these regions had built nuclear technology, or influenced the emergence of treatment-resistant diseases, or generally altered the landscape to such an extent as we have (dams, holes in the ground, big tall chunks of metal and concrete). It is probably in the best interests of anyone living on this planet in the next few thousand years that they have some knowledge of how we've lived and why. "We built weapons that can each destroy land a day's walk wide because there was a war where the stakes were genocide" is maybe something that shouldn't be forgotten. Any number of other developments are also important. It's hard to tell in the moment what will be so in the future.
Another good reason for widespread archival.-
The further problem is that this impermanence is, structurally, a "default" for the current, dominating media - whereas it was only a fraction of knowledge that was lost or vanished when the imperative modes of transmission were "permanent-by-default".-
Further, methinks, we would be missing on a great opportunity - enabled by technology - to make knowledge permanent and accesible - going a bit beyond, from remedial action to constructive action ...
The other side of that goes to impermanence as a feature, the "right to be forgotten" and such aspects ...
... which are also important and in league with the "natural" entropy you rightly point out exists ...
... but the pressing problem is - methinks - on the other side of that spectrum, the side of guaranteeing what up to very recently had been a feature of information media: Its capacity to transcend time, and remain.-