I think you're missing what seems to me obvious, though (either that or I'm very deluded): The DNA molecule is not just an organic compound, but an informational storage medium. Because the genome can be transcribed onto other media (other molecules; modern computers) with minimal loss in signal.
All chemical reactions can be "transcribed onto other media": 2NH3(g) + CO2 ⇌ NH2CONH2(aq) + H2O(l) — media: screen pixels. Dow Chemical doesn't do all its work with test tubes.
The genome degrades and wears away.
Since it clearly hasn't warn away, what has kept it from wearing away?
Edited by lyx2no, : Typ0.
You are now a million miles away from where you were in space-time when you started reading this sentence.