Presumably they'd want to split the sell offer into smaller portions to avoid indicating a turn in the market which might cause a fall in price before they realise [as big a] profit on their position?

Like trying to get out of a place when you see things heading south (ie a calamity approaching). If you run for the door then everyone will see you and the people close to the door might block your exit as they seek to escape. If you cautiously walk, avoid being direct, etc., you've more chance to get out.