They're busy rather than empty. The crossing is when the expedition team runs its lecture programme, when you do your biosecurity check, and when the mandatory Zodiac and wildlife briefings happen. Seabirds follow the ship the whole way across, and there's usually a naturalist on deck helping you tell a wandering albatross from a black-browed one.
There's a framing we use in our pre-departure material that's worth borrowing: your trip doesn't start when you reach Antarctica, it starts when you step aboard. The Drake is part of the experience rather than a toll you pay to get to the good bit.
Practically, it's also when the ship's community forms. People who met at dinner on night one are the people you'll be sharing a Zodiac with later in the week.