[c1ccccc1]

This is your friendly physics reminder that perpetual motion machines have nothing to do with this. It's hard to turn the whole planet into paperclips because paperclips are mostly made of iron, while the planet contains many other elements. Of course, with a high enough level of technology, it might be possible to fuse together the non-iron elements, so that you would end up with just a bunch of iron nuclei. This would even be energetically favourable, since iron is so stable. Then you just have to solve the issue that the paperclips in the center of the planet would be under huge pressure and would be crushed.

[astrange]

It's less than perpetual, but a planet is a lot of raw material to work through for a machine without it breaking down, if the machine's also eaten all the people who can repair it.

[c1ccccc1]

Yes, self replicating machines would probably be required. But self replicators are definitely physically possible.