Wrong. Principles of leadership work much the same regardless of the size of the group being led.
According to Sun Tzu:
1. Sun Tzu said: The control of a large force is the same principle as the control of a few men: it is merely a question of dividing up their numbers.
2. Fighting with a large army under your command is nowise different from fighting with a small one: it is merely a question of instituting signs and signals.
So much for the number of the people being led. Now, concerning the metaphor, "ship of state":
The reason that Plato - and politicians ever since, including a certain Navy veteran named Ronald Reagan - have likened governance of the nation to the "ship of state" is because of the sheer accuracy of the metaphor. The captain never sails the ship by himself - he has to lead, train, and trust others to do so, from the engine room to steering gear, from the navigation department to the mess decks, from sick bay to the men on watch in the night in the bitter cold. The captain is responsible for everything, for making sure they're all fed and rested as necessary, that they're all trained for their tasks, that the level of discipline is sufficient that he can sleep a few hours each night confident that his men won't run the ship aground. Whatever happens on board, the captain gets all the credit and all the blame.
He can't take their hands or physically force them - he must be in turns a cheerleader, a tyrant, a cajoler, a vicious warrior, a kindly gentleman, a diplomat, and - perhaps most often - a remote, mysterious figure whose words are heard only when they are absolutely necessary...for it is he who, even though his hand never touches the wheel, takes the ship where it needs to go, sometimes into harm's way...and, more often, to exotic ports, to a better future, the hope of which being that which gives the sailors the strength to keep going day after day, year after year.
Yes, the metaphor works extremely well, which is why it has stood the test of time for over two thousand years...and it's not me that you're arguing against - instead, you're arguing against Plato and every leader and every president (including Reagan, btw) who has used that metaphor ever since.