I'm disposed to agree with Teo-Je here. Once you're hanging from those nails through your wrists and ankles, with your shoulders pulled half out of their sockets, gasping with thirst, and knowing that this unbelievable torment is going to continue for hours and hours until you die— "Oh, God! Those women can see my penis!" seems like a fairly minor thing.
For my money, the chief purpose of stripping the subject is to transform him into an object of mockery. A handsome young man in a polo shirt and chinos being slowly tortured to death might elicit a certain amount of sympathy from the spectators. But when we bring him out in his undershorts, and then slowly cut those away to the accompaniment of ribald shouts and whistles from the crowd, we make it clear that he's a figure of fun, dehumanizing him and making his suffering a source of entertainment. It legitimizes their enthusiastic cheers when the captain of the guard asks if the sentence should be carried out; and makes it acceptable for them to torment the subject after all the crosses are up, when the public's allowed to come closer.
That slow stripping also allows us to prolong the subject's fearful anticipation of his crucifixion. We crucify our subjects one at a time, so that all but the first have witnessed at least one other being stripped and nailed and raised up on the cross. While his shorts are being cut away, and as he stands naked before the crowd, he knows that he's only moments away from the torments that the previous subjects have suffered and are still undergoing.