What makes iron is the lack of O in Fe~3~O~4~ (that's magnetite, other ores are similar). Carbon for alloying is not an issue it can be easily covered by biomass, you smelt the magnetite by combining it with hydrogen resulting in iron and (very hot) water, no carbon involved, then you add carbon, something like 2% thereabouts, to get steel. Add too much and you get cast iron. The overwhelming majority of coke used in the coke process is not used for alloying, but smelting and reducing the iron. That part of the steel making process is completely decarbonised in the hydrogen process, and the carbon that's used in alloying, well, it's not in the atmosphere is it.

You can rip the oxygen off iron ore with electricity but that's less energy-efficient than taking a detour via electrolysis. It's different with aluminium, there using electricity directly is more efficient.

Sad to day I now understand your point of view. Natural gas wins.

If you think that's what I'm saying then no, you don't understand my POV.