Wouldn't electric reduction cells like those used in aluminium production work as well? Why would you need an input of hydrogen?
There are a few engineering difficulties arising from the high temperatures required and the chemicals around.
And note that aluminum smelting also releases quite a lot of carbon dioxide for various reasons, one of them being consumption of the graphite electrodes.
1. https://en.wikipedia.org/wiki/Electrolytic_iron
2. https://www.newscientist.com/article/dn9878-electrolysis-may... (2006)
3. https://link.springer.com/article/10.1007/s10800-017-1143-5 (2018)
One can imagine electrolyzing iron in aqueous solutions, but I understand this actually needs more energy than producing hydrogen and using that to reduce iron oxide. There is some electrolytic iron produced today, for applications that require very high purity (as high as 99.999%).
There's also a large market for using hydrogen to upgrade petroleum (hydrodesulfurization), but that market continuing to exist presumes some way of dealing with the CO2. Direct air capture, perhaps. There could also be markets developed to make synfuels from CO2 and hydrogen, or using hydrogen to upgrade biomass to get more fuel (hydrodeoxygenation).
There are various smaller markets using hydrogen. For example, making one of the precursors to polyurethane involves hydrogen as a reagent, as does manufacture of hydrogen peroxide.