The main reason Conan in a jockstrap is silly is that the freezing cold climate in his home land would have killed him before he had a chance to get into a real fight.
And when discussing pirates without armor, we should probably keep in mind that in the time period of Jack Sparrow and his piratical colleagues (late 1600s to mid-170s), members of various national navy forces around the world didn't really wear armor either. Fighting in regular clothing was kind of normal. Though naked would have been safer - bits of clothing getting stuck in a wound and infecting it was the leading cause of death for rapier fighters there for awhile.