Um... didn't she ask if they could drop the honorifics and then keep using the honorifics the rest of the chapter? WTF?
When she says "drop the honorifics" she's making a request to shift to a less formal mode of speech.
They were previously both referring to each other as "-san" which is the appropriate way to show respect to someone who is older or a work colleague. Kaori asked Kayoko to drop the formalities when talking to her, because Kayoko is older and Kaori wants to be spoiled a bit. So Kayoko switches from "-san" to "-chan", because that's an expression of closeness to someone younger. It is still considered polite to refer to someone older than you with a respectful honorific, so she stays with "-san"
Dropping the honorifics entirely is something you wouldn't really expect until they're like, family levels of close