It's not the at-sea part that is crowded. It's when you and 6,000 of your new best friends are all trying to get a cab to the airport once you return that is the crowded part.
You got that right. I served on a tin can with a crew of 250. When we were the only US warship in port in Hong Kong, ports in Taiwan and Japan and Subic Bay, P.I., we were treated royally on liberty. When a carrier like the Enterprise came in with 5,000 or so horny and thirsty sailors, you might as well just stay on the ship.