Looking at traditional medicines (Chinese being an easy example), early cultures tried all sorts of weird stuff in the pursuit of medicine
Given that infection has always been a huge danger, and alcohol has pretty much always been around, how did no one ever stumble upon the fact that dousing a wound in booze stopped it from becoming a fatal rotting mess?
Part of the answer is probably that the alcohol solution needs to be 60% or greater to have an antiseptic effect. Alcohol distillation wasn't really explored until the 12th century and even then it was likely some time before they got their alcohol concentrated enough for its antiseptic properties to take effect.
Even once we could distill the alcohol it's not immediately obvious that it would have any antiseptic effect, and dousing an open wound with it would probably hurt more than it would help (it's not only painful, it dries the tissue and delays healing).
I'm not entirely sure this question should be phrased this way. Really, the answer would be that it just didn't happen. That's the answer to a lot of things. Perhaps phrase the question in the positive for better results?
The romans used boiled wine and vinegar to treat wounds.
I think it has to due with the lack of understanding of what caused infection.