occam
Hero
The fact is, ALL swordsmanship requires dexterity. Also strength. Also constitution. Also intelligence, wisdom, and charisma. You want to be good? You use everything you've got.
Katanas no more use dex than longswords, but longswords DO use dex.
Heck, BOWs use strength. I'd argue more than they use dex, but that's not how D&D does it.
Right, the thing to remember is that a lot of these design choices are about modeling fiction, not reality. Finesse weapons exist so that you can have lightly armored rogues and swashbuckling fighters effectively using melee weapons in a game where the default melee ability is Strength. It's also the reason that ranged weapons use Dex (good for stealthy elves), and that light armor allows full use of Dex while heavy armor allows none. You don't want the Three Musketeers wearing plate mail, or the Grey Mouser wielding a greatsword, so you design the game with mechanical reasons for Dex-heavy characters to choose light armor and weapons.
So when asking the question about whether a katana is a finesse weapon in D&D, the answer has almost nothing to do with weight or real-world use. It depends on which katana-wielding fictional characters you intend to model in the game. Are they generally physically powerful fighters wearing suits of metal armor, or are they often lean, highly agile, lightly armored combatants? The answer to that question determines how you design the katana.