Simply put, historically, a blast of heated air was used to thermally decompose iron ore and melt iron. It wasn't possible to mix iron ore, carbon, and get it hot enough by burning the carbon. The exothermic reactions of carbon with oxygen in the air, carbon monoxide with iron oxides, etc were needed to get usable iron. Furthermore, the residual reducing power of carbon monoxide shields the iron from atmospheric oxygen, until a slag can form to also shield it.
Now in modern times, an electric arc furnace, charged with iron ore, scrap, carbon and free oxygen, can work just fine, before the carbon monoxide generation starts happening, anyway.
But in reality, way more is happening than just the reduction of iron oxides to free iron. Even today, iron smelting is as much art as it is science, small amounts of carbon (and other elemental,) impurities alter the crystal types that grow in th pig iron mass, changing it's physical properties.