How old is modern medicine compared to their religion, customs, and traditions?
It doesn't make sense from a modern lens because as modern people we know that his mouth is full of germs and a better antiseptic would be alcohol, but the ancient aim was that a man with a holy mouth that only sings praise for G-d should cleanse the wound to prevent infection.
Not all Jews practice this. The only Jews that practice this nowadays only practice it because they're terrified that altering their customs and traditions to be more modern will cause the heavens to render the decision that there will be another shoah. All the other Jews use straws to suck a bit of the blood out, and they're done.