This is a process for refining iron ore, as opposed to using a blast furnace, or using the same process with decomposed natural gas instead of just hydrogen. In steel production it would be subsequently smelted.
The issue with hydrogen, which was first noted IIRC in the high-pressure Haber-Bosch ammonia production process, in which H2 and N2 at high pressure over a catalyst in a steel chamber forms NH3, is that free hydrogen reacts with the carbon in the steel under these conditions, which caused the pressure chambers to regularly explode (solution was a sacrificial lining of the chambers which was regularly replaced). For low-pressure H2 it may not be much of a problem, but that's not very efficient for transport.
Ammonia combustion generates NOx smog, and ammonia is pretty toxic to store and transport as a gas. For fertilizer it's stored as (NH4)(NO3) or similar.
Hydrogen production has a few major use cases, but replacing natural gas is not one of them. Iron reduction, nitrogen reduction, carbon reduction, in industrial settings, is about it.