This isn't the much feared, general, "banning of books." It would be specific restrictions on specific material in a very circumscribed area. You may very well hold that freedom of information is sacrosanct, but then we'd be left wondering why a "top secret" category is allowed to exist.
Information isn't sterile. It has a purpose and a use. Just as not all photographs are of the same subject matter. These differences allow us to discriminate one type from another, one purpose from another. If someone has a list of credit card numbers that doesn't belong to them, despite a call for freedom of information, I can make the case that they are up to no good and probably a criminal - the probable crime is connected to the characteristics of the information they have obtained.
In truth, we already accept restrictions on freedom of information - when the reasoning justifies the action. To categorically dismiss banning as an option is disingenuous, in the same world where privacy is such a living issue.
It also seems strange to introduce the barn door analogy, as if delete keys weren't on every keyboard everywhere. And frankly, the idea of a ban isn't just to eliminate the information - just as we recognize that not all child porn can be found and scrubbed - it's to help identify and prosecute those who are seeking to use the banned information for nefarious purposes. Putting a ban in place identifies the information as a "no go" area, giving someone the chance to decide if they want to follow a certain path, knowing there is a risk of prosecution for the behavior.