Well, this is fun. We've tried the "War on Immorality" many times, and that's just in American history. I hate to keep using the Prohibition example, but it fits, when you try to legislatively choke off the supply for a product for which there is such a high demand, as admitted by the good archbishop when he called porn a multi-billion dollar industry. Just as when alcohol was outlawed in America, organized crime took it over, made money hand over fist and grew in both power and influence. The same thing would most likely happen with porn if the archbishop got his wish.
You can also use the Comstock laws. Their biggest contribution to American history was to make Margaret Sanger a celebrity.
You're talking about apples and oranges.
Prohibition was the prohibiting of a permitted substance and one which, furthermore, had a long and positive history in human culture. That said, if you know anything about the 19th/early 20th century, it had obviously become a problem in the unrooted US culture of the time, so I can't say that Prohibition was necessarily a bad idea at the time. But it was unworkable, simply because there is nothing wrong with a bit of moderate consumption of alcohol and this has been part of human culture since the dawn of time.
On the other hand, pornography was never acceptable in the US, and has never been completely acceptable anywhere else (which is why even early 20th century French dirty old men had "secret" collections in their dresser drawers when they died!). Beautiful images of beautiful people are one thing; pictures of people doing disgusting things with animals, being tied up and beaten, or torturing children are an entirely different matter.
If the Archbishop gets his wish, everybody in the US and the world is going to have to ask themselves (a) exactly what are they watching and why are they watching it? and (b) is that the kind of person they want to be? Questions that need to be asked, IMHO.
Did you ever read, De Tocqueville ?