Increasing the drag at low speeds would change this behaviour. This already happens a little bit but could happen more. (Unfortunately, I think the skin drag slider in the UI now doesn't have any effect.) This would also make getting under way more difficult. Really the question is, how long should it take a ship like this to slow down?
And it might be worth distinguishing two situations here. In one, the helmsman is keeping the ship pointing straight; in the other, it's drifting and likely to turn off to one side, which should slow it down more quickly.