But carbon in steel is in steel, not the atmosphere, so we don't mind, no?

Alloying carbon represents a minute fraction of coal use in the steel industry. The vast majority is used for heat and reduction of iron ore (removing oxygen). This carbon addition does not release carbon dioxide (at least not directly, some is released in the coking process, but that process can have its own improvements). When people talk about replacing carbon in steel production, they are talking about the fuel coke.

> No research is going to replace the carbon in steel with something clean

Is that what you meant to say? How is carbon in steel not "clean"?

I see, thanks for the clarification. Yes, I was thinking of coal solely as a source of energy (heat, specifically) to melt steel.