Our assumption is that within the context of chat, it’s generally helpful to know whether folks are present or not, since it’s a more synchronous form of communication.
It seems reasonable that the “Hide my public profile and presence features” should also apply to chat, but we haven’t done that yet and are thinking through the implications of this and what kind of reciprocity should be implied with presence features in chat.
I don’t know that we’ll make the ability to disable presence site-wide a feature. But if you really want to use chat and globally hide presence on your site, you may be able to work around this with some CSS.