Steel is much more complicated than that (as I'm sure you know), and the important properties come from the relative quantities and arrangements of iron crystals and several types of iron-carbon crystals. Interestingly, hot iron is not soft because it is semimolten, non glassy substances like iron have sharper melting points than that. When you heat iron to an orangeish glow, much of it converts to austenite, which is soft and nonmagnetic (smiths often keep a magnet stuck to their anvil for testing iron), and depending on how it's cooled, more or less of it is converted to martensite, which makes good blade steel. If you quickly cool it to ~500 C (if I remember right) by putting it in a bath of certain molten salts, it stays flexible, but does not glow, and can be handled (carefully) with thick leather gloves, and easily bent over your knee (or more commonly, straightened). Also, for the purposes of our discussion, true iron (with no carbon) doesn't exist at all. That didn't exist before the modern era (some people say the romans used it, and the technique was lost). There's just good steel and bad steel. Only certain formulations of steel are useful, if you have too much carbon, you get cast iron, which is used for casting because excess carbon lowers the melting point and makes it flow better, but is too brittle to be good for much else.
Also, I didn't know that geothermic smelting was even possible before this thread, so I just accepted it as possible in the DF world. I doubt irl geothermic smelting has much in common with DF's magma furnaces anyways.
It has nothing at all in commong with DF magma smelting, and the comparison makes no sense. IRL geothermal smelting is for aluminum, which is smelted with the Hall–Héroult process, which uses electrolysis, and requires ridiculous amounts of electricity. Iceland, because of their shallow magma, can cheaply produce way more electricity than they could ever really use, so they import bauxite (not normally economical) and export refined aluminum. Not geothermal smelting really at all. Just geothermal electric plants powering electrolytic smelters.