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.
That's like saying "5 years away is far enough that Mount Rushmore might be gone by then!" because we could nuke it if we wanted to. Why would we do that!? We like the moon being there! Do these examples really help illustrate how far away 800 years, or 5 years, are?
Lots of people want to build megastructures, and the moon is convenient material; I suspect that when the capabilities make it seem like a serious possibility, people will discover the problems and then do it anyway just like with almost all the other environmental issues to date that compete against economic interests.
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).
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.