But I don't think it degrades to the point where it actually is worth throwing it all away.

It's not only that data becomes more scarce. It's also that it becomes noisier. Case in point: many people believe the Gospels to be a semi-accurate narration of what happened during that era, but actually they were compiled centuries later, and historically contemporary source are both scarce and painting a completely different pictures.
The furthest we go, the higher the possibility of having bogus evidence.

Is this a serious question, or a statement of anti-epistemology?

A bit of both, I guess. A cautionary tale, but also a question I would definitely make if I were discussing with someone with that point of view.