Or a perfect example - because there are extremely few cultures and circumstances in which very old human graves are moved when the government or rulers changed?

Graves generally aren't permanent; most plots are leased for a fixed term. What is done with the caskets and contents thereafter varies widely.

Is that really how pyramids worked? King Tut in the pyramid for 60 years then to the Nile his bones?

It sort of worked like that, though that wasn't the intention? By which I mean, as I understand it, all the pyramids were robbed a very long time ago, but Tutankhamun's tomb survived undisturbed until the 20th century because it wasn't in a pyramid.