First, I don’t see a reason why just a name would not be good enough as opposed to the mug shot itself.

Second, it seems that this same justification could be used to justify a lot of privacy breakdowns. For example:

Question: “Why are the suspects naked in the mugshots?”

Answer: “This is actually a civil rights thing to show that they were not beaten up during their arrest. Before, police would hit suspects where their clothes would cover the injuries, but with naked mug shots published on the Internet, they can’t do that any more.”