Well first, One Piece pirates are far from your average caribbean pirate.
Thing is they take pride very seriously (the men at least). Like what Sanji and Zoro said, they would rather die than be humiliated, which is exactly what happens if you don't accept the challenge. The Davy Back challenge leans more to defending ones pride rather than gain more crewmembers. Though since the Strawhats have such a strong bond with one another then they are risking far more.
Also, Zoro is really honorable. Guess it goes with his swordsman code or whatever. If they lose a match and they pick Zoro then he would no doubt accept loyalty even though he probably could easily singlehandedly defeat the foxy crew. As for the other pirate crews who do the challenge. If one team loses then that should mean that the opossing pirate crew is greater in strenght so no doubt if there is a mutiny with the selected crewmember, he would surely die so it would be wise to accept the loyalty.
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