I'm sure plenty of Asians have been killed by wooden swords. I'm also sure a whole hell of a lot more have been killed by swords of a better material than wood.
The point is, a wooden sword just isn't going to cut as effectively as a steel or better material sword. Even your example of a folden steel sword vs a damascus steel katana could be used. While the difference in damage and will be far less than comparing wood to steel. You can still achieve a sharper edge on folded steel than you can damascus steel, allowing for greater ease of cutting.
That for example is one of the leading reasons that diamond scalpels, or at least diamond edged scalpels are used in surgical procedures instead of just plain steel, they can hold a far more "honed" edge, than a steel scalpel can, allowing for less pressure required to make an incision and a much smoother, cleaner cut. Here's a paragraph taken from a diamond scalpel manufacturer.
Quote:
The SPI Supplies Brand Diamond Scalpel Blades
Produced from the finest quality natural diamonds, these blades are extremely sharp, requiring minimum pressure for penetrating and precision cutting without the distortion normally associated with the use of stainless steel and other materials. Titanium handles make these knives lightweight, perfectly balanced and corrosion resistant for long life. Safe to sterilize up to 140° C ( 284° F).
Material Hardness, Radius of Curvature, and Distortion There is a bit more to the story on "distortion" because it all boils down to radius of curvature at the edge. We are talking about the very end of the edge, not the "angle" normally reported in the knife specifcations. For example, if we are talking about diamond knives for ultramicrotomy with a 35° angle, the radius of curvature is the measurement at the actual edge. The smaller the radius of curature, the "sharper" the cutting edge. And the sharper the edge, the lower the forces needed for cutting which of course results in minimal distortion and other damage at the cut surface.
So now we come to the reason for diamond and not some other hard material, such as tungsten carbide or silicon carbide. The smallest possible radius of curvature in any material is a function of its hardness, the harder the material, the smaller the smallest radius of curvature possible in that material.
And therefore the advantage of diamond becomes much more clear: A smaller radius of curvature can be produced in diamond than in any other material, since after all, diamond is the hardest material known. And that is why diamond translates into substantially lower cutting forces, resulting in far lower distortion than would otherwise be possible. This advantage is at once evident when cutting most tissue samples.
I really see no reason why a copper falchion should do as much damage as the Volriani Blade(an adamantite falchion), or why a steel pike, should do as much damage as the Mottled Lance(adamantite lance) it makes no sense, in either world, and completely diminishes and takes away from the whole "legendary mystique" that those weapons carried around with them for so long. Now they're just ordinary old weapons, which really aren't any better than there regular old tanso steel counterparts. Why even bother with them?