Nice! I’m guessing they have room for more weapons because the intended mission is more regional defense of South Korea than the global missions of US ships (more missiles, less fuel tankage). But that’s just a guess.
Exactly right. You don't get something for nothing. Especially true in ship design. US ships are built with a balance of firepower, survivability and range. Your probably right that they sacrificed fuel capacity for firepower. Not a bad choice given their requirements. I'd feel better if we provided our Cost Guard similarly.
It's a good guess. US destroyers are designed to be deployed at long distances for extended durations. This means a lot of storage for food, fuel, spare parts, repair facilities, etc. A ship that doesn't need to be out at sea for more than a few days at a time, and not more than a day's sail from port, can use most of that freed up space for weapons, sensors, and electronics