If hyperinflation brings that date closer, the dollar will probably also stop being a global reserve. Or possibly: will be caused by it ceasing to be a global reserve.
Wait, what? 800 years is absolute peanuts for the fate of orbital bodies. Wikipedia's Timeline of the Far Future estimates the demise of the moon in 7.59 billion years; still in orbit around the Earth (albeit a much higher one), it gets destabilized by the expanding sun and eventually swallowed by it, along with the Earth. If they aren't swallowed by the sun, they estimate 65 billion years before we lose the moon in one way or another.
Even the unit of replication is a factory under human control with no novel AI, and which can only replicate with significant human oversight of already existing mining, processing, and manufacturing equipment, it doesn't take insane reproduction rates to disassemble the moon in 800 years.
However, the main point of the example is "800 years is too far ahead to plan for how much the US dollar might inflate" by way of demonstrating how extreme things can change. As far as I know, no fiat currency has existed that long, and only three country-like entities[0].
Mount Rushmore isn't likely to be targeted by nukes, but I strongly suspect that it is defended against vandals (politically motivated or otherwise) with dynamite (or similar categories of explosives) — that said, if you've always wanted to go and have not yet done so, you should, as I could've said much the same thing about the World Trade Centre 22 years and a fortnight ago.
(I wonder if a single unfriendly nuke on US soil would cause an economic shock? Normally the assumption would be what else might come with it).
[0] https://www.brainscape.com/academy/longest-lasting-empires-w...