At the level of abstraction that D&D works at, one single handed sword is pretty much the same as another, whether we call it an arming sword, a saber, a broadsword, a khopesh (which is really an axe), a hanger, spadroon, spada, or dao. I think I'd prefer to keep it that way, at least in the simple base rules.

Likewise, I'd really like to see the base armors be leather/padded, brigandine, chain mail, and plate armor.

I'm sure there will be, and I wouldn't mind owning, an Ultimate Arms & Equipment Guide that expands on the base definitions, but, as I assume there will be, it includes double weapons, I will continue to ban them.

And if the katana does superior damage to Western weapons of similar heft and length, I will either add a breakage mechanic or nerf it.