The purpose of the clock is going to get lost, and eventually there's going to be holo-documentaries on how the 20th century "Americans" predicted the end of the world.
The fact that it's dug into a mountain and has multiple large chambers definitely won't help make it seem scientific and not archaic, mysterious and cultish. I swear they are taking cues from novels.
In 10,000 years, humans could repeatedly cycle between "Stone Age" and "holo documentaries". Civilization as we know it isn't that old, technological civilization even less so.
I don't have a citation, but I've read that if we fall, we won't get back up. The easily mineable metals, minerals and fuel sources have been used up - starting again from scratch would be incredibly difficult.
(Larry Niven addresses this somewhat in his novel The Mote In God's Eye. I can't really elaborate without spoilers. :P)
I wonder how viable that is. In a world where we're considering sucking oil out of sand and stealing air conditioners for $2 worth of copper, I'm surprised there aren't more landfill reclamation projects - so maybe that's strong evidence that landfills don't contain as many goodies as we think.
Plus, you're not going to find coal or oil at a landfill, except in the form of plastic.
For many materials, I think landfill mining is a lot more viable than mining from ores, both on the basis of high concentrations and on the basis of higher energetic states. I mean, you're not going to find native iron, aluminum, titanium, or silicon in rocks, and cullet is a lovely material for making glass from. And, in most of the world, you'll find a lot more platinum and tungsten in the landfill than you will in your local rocks.
Energy and helium are the only resources we're currently consuming. The others are just being reversibly transformed.
Mining landfills is dangerous work, but it can be automated. Mining in general is dangerous work, but I suspect that landfills are even more unpredictable than rocks. Landfills contain smallpox virus, polychlorinated biphenyls, HIV-contaminated hypodermic syringes, and so on.
I think that current landfill mining is limited largely by aesthetic considerations (and the resulting laws), not pure self-interest.