In Western society "escorts" have always maintained the legal fiction that they solely offer "companionship" services in order to escape prosecution/social stigma. In reality, escorts have sex with their clients 99% of the time because that's what clients reasonably expect - one would have to be quite sheltered to take the "companionship" story at face value. Although one might take an "escort" to a social function for her elegance and conversational ability, her real role is the sexual service she provides.
Given the taboo associated with exchanging sex for money, isn't it quite likely that geishas were actually sophisticated sex workers? Isn't it quite likely that - like Western "escorts" - geishas maintained the outward impression that their primary role was "sophisticated companionship" whilst the tacitly acknowledged reality was that the service they provided clients usually included sex? Further, wouldn't historical sources from the period be somewhat naive about the actual practices that occurred because of the uptight social mores of the time? Is the Western notion of the geisha as primarily a "sophisticated companion" who does not offer sexual services merely a myth that started when naive, prudish Western people recorded their observations of Japanese culture?
No they didn't have sex for money, they did exactly as it's written on the jar, extremely sophisticated societal company for tea ceremonies and the like.
The idea of them being prostitutes came post WW2 when Japanese prostitutez were dolling them selves up as Geisha in order to get clients without being actual Geisha