Fact is, these categories have been largely artificial since day one, anyway. "Longsword" is a remarkably broad descriptor. (Insert, "No, that's a broadsword!" joke here.) Anything that we could call a bastard sword could just as readily be called a longsword in most historical contexts.
In 5E, the game doesn't require a separate bastard sword entry, any more than it requires a separate broadsword entry. They're both covered by "longsword." The differences are entirely narrative.
(And for the record? The katana really isn't any more or less a Dex weapon than the longsword. IRL, both traditions had lots of tricks and quick moves. There's just no reason for the katana to be anything other than a longsword in 5E.)