It's not sharper. And there are lots of curved swords - cutlasses, scimitars, scythes, those Klingon things.
But even if it was sharper, are you saying that being stabbed in the face with a katana is somehow worse than being stabbed in the face with a longsword? Both are going to kill you equally.
It is sharper, the steel is tempered so the edge of the blade is harder, and harder steel is the sharper an edge it can keep. It's the same concept as a titanium knife can be sharper than one made of bronze. I have put a good amount of time studying Katanas, as they are my favorite of weapons.
I see your point on the second line though, but still, I can see flaw with it in my opinion. Both being stabbed with a katana and a longsword would be deadly, but a katana's sharp edge might be better at it than a dull longsword (Or vice versa, depending on which is sharper atm, though for game mechanics, I'm suggesting we always assume that a katana is sharper than a longsword). And with the logic you suggest, all swords should deal the same damage, no matter what, their all swords and thus equally deadly. I have a good example, I have a knife and a pencil, and decide to go hunting. Now, I find a feral pig, now both might do piercing damage, but it's safe to assume that the knife would be better at the job than a pencil.
Oh, and by the way, those "Klingon things" you refer to are bat'leths, and don't do slicing damage, but piercing damage. Unless you are referring to a Reverse bat'leth, which do exist, but are less common.
