I don't think people understand how Maiko/Geiko are treated in Japanese culture, which is... surprising, like, we're 169 chapters in, guys. C'mon.
You are an escort basically, yes, but they're treated with SO much respect and reverence. It's not like you can hire a maiko or geiko for a dinner party (keep in mind the flower fee is around 50,000yen PER maiko, that's about $500 for her just to show up to your dinner party, not for the cost of dinner itself either. A mid-tier geiko, like Momo-nee-san is probably closer to 200,000yen/$2000. That's for maybe an hour or two of just her company) and then make sexual remarks or man handle her or whatever. She'll sit beside you, she'll refill your beer, listen to you gripe, dance or perform for you, play drinking games with you or compliment you.
You CANNOT outright pay a geiko for sex, it is NOT a service you can purchase. She can certainly suggest a sexual relationship, but only if she wants to (and yes, it does usually come with the expectation of a gift, maybe not necessarily money, but certainly something like new jewellery, new kimono, etc.).
Maiko/Geiko are traditional hostesses (btw you also can't 'buy' sexual services from hosts or hostesses) basically, but also double as actresses and performers.