The carbon content of mild steel is low but not insignificant. Pure wrought iron [0] is a dream to forge and it has a huge grain structure. It's more ductile than mild steel but it's also not as hardenable or tough as mild steel [1]. That little bit of carbon in mild steel makes a big difference.
[0] I mean real wrought iron -- the almost 100% elemental stuff -- like the Eiffel tower is made of. This is practically unobtainable today. The "wrought iron" you commonly see for sale nowadays is always mild steel. And "cast iron" is actually very high carbon steel, not iron. Cast iron so high in carbon that it's brittle and cannot be forged or easily welded.
[1] It's a myth that mild steel cannot be hardened. With a proper wetting agent added to the quench, you can harden it significantly.
Wrought iron and mild steel are more or less functionally equivalent. One other reason why cast iron is so brittle is because it contains quite a bit of silicon.
[0] I mean real wrought iron -- the almost 100% elemental stuff -- like the Eiffel tower is made of. This is practically unobtainable today. The "wrought iron" you commonly see for sale nowadays is always mild steel. And "cast iron" is actually very high carbon steel, not iron. Cast iron so high in carbon that it's brittle and cannot be forged or easily welded.
[1] It's a myth that mild steel cannot be hardened. With a proper wetting agent added to the quench, you can harden it significantly.