The earliest refining of iron also produced a little steel as a byproduct. There is reason to believe that iron refining is as old as, or even older than bronze, and steel would have been made with that iron. However bronze was easier to work with (I think this refers to readily available ore though I haven't looked into this and could be wrong as to reasons). In general a craftsman would use bronze where possible, iron where bronze didn't work (which wasn't often, bronze is better than most people think), and steel only where required. For files and other metal working tools not much steel is required and the advantages would be worth it (though these might be case hardened iron - we suspect they knew how to do this long ago but there is no historic record to be sure)

The are plenty of stories passed down about magic swords that could cut others in half. If someone collected enough steel from the little that would made it would be magic compared to other swords, but the effort to collect that much steel would be enough that few such swords would be made.