In my engineering classes, we were taught that with forgings, the grain pattern is effected, and a "grain flow" follows the outline of the piece:
In a milling process, the billet's grain flow is in one direction, and the milling cuts across it leaving weak spots where stresses can cause fatigue. Like this:
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The forged pieces are usually tougher. That is why you want them for piston rods and other high stress parts.
There
are post machining processes that can approach forged pieces. But it is my understanding that they are very difficult, and very expensive. I am not sure how many sword manufacturers would have access to such high end equipment.
"A sword never kills anybody; it is a tool in the killer's hand." Lucius Annaeus Seneca 4BC-65AD.