Quenching and tempering steel is a pretty complex thing, involving a number of different phases of steel that have different types of molecular matrices. The idea is to get carbon atoms to migrate into the steel matrix at high temperature, cool the steel fast enough to prevent the carbon atoms from migrating out during quenching, and then relieving some of the internal stresses by tempering. All this while trying to prevent grain growth.
Genuine katanas are made from tamahagene steel which is produced by smelting iron sands in a small bloomery. But unalloyed steels like tamahagene have to depend entirely on the complex forging, quenching, and tempering processes to purify the steel from impurities (which are high in tamahagene) and produce a hard edge that isn't brittle.
Historically, tamahagene wasn't the best steel for making a sword, not even close. It's just what they had to work with. The best sword steel was the steel that the Toledo swordsmiths used. The Toledo process, which took centuries to perfect, produced the best very best swords in the world and was the gold standard for centuries. The Romans started using Toledo steel when they found out about it. Both Damascus and Japanese processes were unsuccessful attempts to duplicate the properties of Toledo steel using inferior materials.
Unfortunately, the source of the steel used in the Toledo process is not known, and the process itself, just like the authentic Damascus process, is lost to posterity. Only the Japanese process remains. Only in the last few years have we been able to produce sword steels that are superior to Toledo steel.
