Can unicorns/hype/mystique last since for a long time? Sure! How about since the end of the iron age?
Perhaps we are speaking cross purposes a little? I am 100% down with what you are saying. I recognise the skill/craft/art that goes into all the steps (smelting the steel, forging the sword, polishing the sword - there are probably more). And these are not the same artisans: "many hands make light work"! I think this craft is valuable and is worthy of respect!
The subtlety I am trying to introduce is that the aesthetic beauty of a sword is a function of the artesans and not necessarily the material (tamahagane).
Tamahagane is decent steel that comes with baggage... The bloomeries didnt get hot enough to liquefy the iron. If you can melt the iron/steel, you can make it homogeneous and scoop the slag off the top of the liquid. Not so with blooms... Folding was used to compensate for the heterogeneous nature of the blooms and the large presence of 'impurities'. By folding many times the steel becomes more homogeneous and some of the 'impurities' are removed. Why do I use the scare quotes? Well.... what are impurities?
@inferno is probably right. Im not sure - I don't know enough about blacksmithing... Those furnaces were a mess of iron, sand, steel and charcoal. As I understand it... 'impurities' in this context are the more macroscopic things (a.k.a slag, sand, charcoal).
I don't know if you can reduce the phosphorus content (using these methods) if it is present in the ore? 1
Anyway... the material informed the process... the process informed the art (and no doubt there was a feedback loop). We have better materials now... But we can choose to retain the process. I don't see why an artesan couldn't start with a better quality steel, fold it several times (adding impurities if they wished) to produce a nice hada.
Maybe I am wrong. But I bet it is theoretically possible to make a sword that is visibly/practically
indistinguishable from tamahagane swords using modern materials 2. Sure... It wouldnt be traditional. But it would look pretty. If so, surely that would rob tamahagane of any special status. If it has any, it is that it is a cantankerous, contaminated steel - like any other bloom steel - that is difficult to work with and does not offer any intrinsic benefits (functionally or otherwise) other than being labour intensive and lower quality than the modern alternatives. That in no way takes away from the artistry or is a slight on Japanese blacksmithing. It is an elegant solution given the technological constraints civilisation faced at the time... But it isnt the iron age anymore. ~1200 years have past! We can do better. And THAT is why it is romantic to me... Not everything has to be perfect or made by a machine.