How does this fit into the wider picture of steelmaking with electric arc furnaces? Those have been around for a good long while; what can this do that an electric arc furnace can't?
That’s the historical reason, but now it's used because carbon is a reducing agent that binds to oxygen, preventing it from oxidizing the iron back into iron oxide and because the coke is used as a permeable membrane to let the resulting gasses escape.
If it was just a matter of heat, there's any number of cleaner fuels steelmakers could use but they can't because the coal serves an important role in the chemistry of blast furnaces.