My master smith (I was an apprentice once) kept (and probably still keeps) his anvil face to a mirror finish. Also his hammer faces.
It's good practice to have separate forging and driving hammers. Keep one set of hammers polished and only use them on hot metal. Keep another set for hitting chisels, punches, and such.
Perhaps you once complemented someone and that person joked, "Flattery will get you nowhere." Well, in blacksmithing flattery will get you somewhere. That is, if you have a hammer called a flatter. It is of a class of handled tools called set tools - they are set on the piece of metal and hit with another hammer.
A flatter looks like a small sledge hammer with a big square plate welded to the face. The face of the plate is mirror polished and curves up slightly around the edges. You can work your knife between the flatter and the anvil and get the regular hammer dents out of it. Saves a lot of time.
My old master smith was so deft with his regular hammer that his work looked smooth like it was injection molded, right off the anvil. He was a classicist.