> While cases of Jake Foot went through the roof

Jake Foot was caused by a change of ingredients to Jamaica Ginger, which had been a popular cold remedy in America for over 100 years. It was caught almost immediately. And while Jamaica Ginger, along with many other patent medicines, was indeed a popular alternative to hard liquor[1], it was also consumed by many Americans (quite possible a majority--it was the Nyquil of the 19th century), including children. Only a single dose of Jamaica Ginger was required for paralysis or even death, and this why children were among the many victims. There were other cases of organophosphate poisoning around the world, some much worse, that had nothing to do with Jamaica Ginger or Prohibition. Jake Foot is just another story popularized in support of the mythology of Unintended Consequence in which anti-government conservatives, and now liberals, love to revel.

You also greatly exaggerate the number of methanol poisoning deaths from the infamous government-sanctioned liquor adulteration scheme.

All-in-all, the number of deaths in both cases don't seem to exceed the number of reduced deaths from cirrohsis alone, let alone all the other alcohol related deaths. It's difficult to exaggerate how much Americans drank prior to the institution of Prohibition, and more importantly the extent of the public health catastrophe that had long been unfolding. (And the peak came well before Federal Prohibition as state Prohibition laws had already become common, so looking back merely to the 18th Amendment doesn't properly capture various causes and effects.) There's a reason the country passed a constitutional amendment, which is, to say the least, not something that happens regularly; it requires an uncommon degree of political consideration and agreement across the population, testifying to how significant of an issue it was.

But, as I said, Prohibition as enacted may indeed have been too expensive. Not because in a simple statistical sense there were more net deaths from Unintended Consequences(TM) (which is almost certainly wrong), but because it had the effect of changing the demographics of death. Increased criminality resulted in more highly publicized random deaths of bystanders who might have never touched alcohol. As with terrorism, the archetypical example, people respond in an exaggerated manner to things which they feel they have no control over. As has been shown time and again, the middle class is more than willing trade the well-being of the poor for improvements in their own quality of life; and that exchange can happen both when prohibiting something but also when permitting something.

There are other lenses with which to view this. Prohibition was at its heart a feminist movement designed to and arguably quite successful in reducing spousal abuse and economic impoverishment of the household.

To say "prohibition doesn't work" is trite and easily falsified. There are all kinds of cases where prohibition works like a charm for its intended cases. Take, for example, drug trafficking in Singapore. The question is whether the result is worth it, and very often the answer to that pivots on a qualitative analysis, not quantitative. But people want to avoid qualitative analyses because it requires making moral arguments which are much more difficult to justify, so you end up with a bunch of junk quantitative "science" to justify a position, and that tactic is just as available to "bad" people as it is "good" people.

[1] See this article from 1900 about a group of woodsmen who overdosed on Jamaica Ginger: https://timesmachine.nytimes.com/timesmachine/1900/04/16/101... Maine banned the sale of liquor in 1856.