Basically, every weapon is designed for a certain age, and a certain use. It isnt likely to be much good in a time where the requirements are different.
To use the example of the bunch of reeds: A katana will cut it in half, but put it inside a steel pipe and it wont do much harm. An axe wont cut the reeds, unless its exceeding sharp, and youre very lucky, but it will hack through and crush the steel pipe.
The main reason katanas are so famous is that they are among the last main weapon swords made. Most of the world had moved to swords as a last resort type of weapon (well, not last, but you know what i mean, i hope), which means that they were rather crappy. The katana outshone those with ease, since it was also effective against the armors used at that time (which in most of the world were rather ineffective by that time thanks to firearms)