I cant remember where I did read that, but it was an interesting article on the net about "nakedness in ancient times" and how we look upon it today - the conclusion was, that in Greco/Roman ancient times nakedness was far more common and "natural" than we think today - not only because of the climate, but for tradition. The Romans borrowed many ancient traditions from the Greeks. Starting with sports/exercises in nakedness n the "school" (gymnasium), to theaters, hard labour in corporeal work in nakedness (not only for slaves), to the arena, to the orgy... and so on.
So I think the nakedness of a victim when it came to punishment/torture/execution was not exactly unusual. Regarding the crucifixion of Jesus many scholars set their focus on the special "jewish traditions", even Pilate and the Romans could not overcome, and their "teaching against nakedness" and argue, that may be the reason why Jesus (and other victims) would have been granted a loincloth to cover the nakedness, when he was crucified near Jerusalem. I am not sure about this.
I think, to feel ashamed when being confronted with nakedness is a newer phenomenon that is closely connected to the upcoming rule of christian religion and their "moral teachings" over the centuries dominating after the Roman empire. But that happened after Jesus execution and even we, in modern times, are still under that influence and it is internalized, that nudity is something ... improper to "show" - a rule, thats now permanently present in art, movies, depictions of all kind - despite all "liberalism" we have today.