Sweden is actually the first country to build such an plant. Att the moment it is mostly testing plants but the real ones will be built soon. https://www.hybritdevelopment.com/
EDIT: I should have read the article first.
From memory efficiency was 4.5kwh/kg. At 12 cents/kwh that's $0.50/kg.
Seems like a better idea to do that than to pretend hydrogen is 'green'.
You need about 54kg of hydrogen per ton of iron. Assuming it takes 50 kWh of energy to make 1 kg of hydrogen, you get something like 2.7 kWh per kg of iron. This is significantly more energy efficient than the idea you're proposing.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6918249/
The Norwegian pilot plant used a crude asbestos separator for the anode and cathode. The above used some magic polymer.
They got it down to 3.53 kwh/kg