There's (admittedly comparatively expensive) alternative processes, and even if you stick to the old process and just stop using coal for electricity generation you'd cut coal use by 75%.

Not to mention, the carbon that stays in the steel doesn't actually go into the atmosphere, so there's less CO2 emissions for that specific use if you can substitute the fuel used for heating.

you're probably talking about direct reduced iron and it's really a problem that can be dealt with easily, just chuck a piece of coke when it's molten for the second time in electric arc furnace (and maybe electrodes introduce enough carbon). substituting coke with hydrogen works also on "ingredient step" if you mean by that fuel needed to reduce iron ore to iron

maybe there's a way to make electrowinning iron economical, and it'd be pretty green too, but i don't know if it is workable

e: you can also avoid need for met coal if you use methane or syngas for direct reduced iron process