Planes aren't filled solidly, though. They are more like a shell around a volume, so I'd think the mass would rather scale like the surface area than the volume

Planes aren't filled solidly, though. They are more like a shell around a volume, so I'd think the mass would rather scale like the surface area than the volume of the plane. Beside that, I would agree that it seems impossible to get such a solution working in dimensions of dozens of meters. A pun: maybe they just took "do things that don't scale" too literally? ;)