Except this isn't actually true. The katana evolved from the tachi during the Warring States Period. The only major difference between early katana and tachi were how they were mounted and carried. Edge up is katana. Edge down is tachi. It isn't uncommon for early blades to be remounted from one to the other. The katana replaced the tachi because edge up became preferred. It put the swordsman in a good neutral middle guard after the draw, not an awkward hanging guard (as with a saber but without the saber hilt's protection to the prominently located hands).
Not all katana are alike though. Because the katana form survived through the relatively peaceful Tokugawa shogunate that followed the Warring States Period, some are definitely more warlike in construction than others. Length and curvature varied a lot with peacetime swords being shorter and straighter than wartime swords.
