...how do you know that doesn't work?

Sometimes surprising and interesting things happen when you experiment. Maybe goat piss with hair of a virgin seems weird, but burying shit in your backyard for awhile, digging it up, and mixing it with burnt wood seems pretty odd too when you think about it.

Is that a recipe for gunpowder?

It seems to be missing sulfur, but otherwise - yep.

If memory serves, one of the big reasons for Britain’s naval supremacy for a long time was their discovery and exploitation of large deposits high-quality of saltpeter in India. Before that, they had “saltpeter plantations” with rows of organic waste soaked with human an animal urine and left to dry in the sun. Before that, it was groups of the King’s men going around the countryside and scraping the stone foundations of buildings and cemetery monuments.

My point exactly; people really like to equate "unscientific" with "turned out to be wrong". Chemistry is such a huge field that it's a small miracle we managed to figure out at all, no small thanks to Boyle who actually introduced the very concept of chemical elements.

With an incomplete knowledge of chemistry that wouldn't necessarily be an irrational experiment. For example, urine was a common source of uric acid in pre-modern times. When applied to copper it would produce verdigris. It might be a reasonable hypothesis that whatever allowed urine to change one metal might indicate that it could change other metals into gold.

But it won't produce gold, same like applying aceton to concrete won't produce antimatter.

You don't perform a scientific experiment because you know what the result will be. You perform the experiment to find out what the result is. That's how science works.