Show me numbers.

OK, how about the number "1"? It's estimated that a shell of very-low-density "statites", surrounding the sun at the distance of Earth's orbit, would require as much mass as can be found in one large asteroid. Increase the mass per statite by two orders of magnitude, and you can still build a swarm with cross-section larger than the Earth.

We can quibble about materials and about long-term stability. It might be that, without constant care, intricate megastructures on an interplanetary scale will collapse or disperse after a few thousand or million years. But to say they are physically impossible is somewhat obtuse. Consider the natural asteroid belt. It is already a type of "structure" - a toroidal region of space populated with a million distinct objects, with total mass something like 5% of Earth's moon. So tell me why a colony of mining robots, digging into the moon and shooting ore off to space factories, couldn't produce a comparable archipelago of artificial space objects?

The specifics of various proposals may be infeasible - e.g. the idea of a solid, rigid Dyson sphere - but I don't see the basic idea of massive engineering in space being shown to be comprehensively impossible.