Hi, English isn’t my mother tongue so I was asking myself that question since I first encounted a w/… Back then I was like: “What tf does ‘w slash’ stand for?” And when I found out I was like “How, why, and is it any intuitive?” But I never dared to ask that until now
As others said, with as w/ was around as part of secretarial shorthand, which got taught to most people keeping corporate documentation and it stuck.
There are a lot of abbreviations like that in the English language that came from abbreviations in written form due to the media in was written in, whether it was newspapers, telegraph, handwritten shorthand, or computer based. It may not make sense because English isn’t a language designed to make sense; it isn’t even designed.
To be fair, no living language is.