There is a scene in "The State of the Art" where the Culture folks visiting Earth are having a party and someone (while wearing a Star Trek uniform and waving a lightsaber around) announces that he wants to be Captain of the GCU Arbitrary.
Someone else comments that a person trying to take charge of a Culture ship is like a intestinal bacteria trying to take command of a person.
Edit: Of course, the Culture also appeals because of the much higher ambient humour level in the Culture than in the po-faced Federation.
