Doesn't seem thst simplistic to me.
Remember that this is an evidence-based argument - we don't need to guess, we can look at the world today and back into the past and see that when something (anything; not just alcohol) is restricted, up to and including the ultimate restriction of supposed total prohibition, it not only doesn't remove the desire for the prohibited thing, it may well increase it and cause a whole host of unintended and unwanted knock-on effects beside. (Organised crime in the Prohibition era being a prime example). Human nature makes it so - nitimur in vetitum.