I agree that manners, than and now, are meant to make people feel comfortable in social situations. I agree that Emma might have agreed, out of friendship for Harriet, to be introduced to Mr. Martin, in whom Harriet has such esteem. However, the tenor of the rest of your post has me concerned.

I have been unable to find the archived post that was pointed out in another context, so please bear with my scattered memory. I seem to recall one of the Pemberlean experts quoting a contemporary etiquette book's advice on acknowledging ladies on the street, accepting acquaintances, leaving cards and the like. I remember it being rather the opposite of what you are implying. I believe allowing the introduction would require Emma to accept Mr. Martin's acquaintance in other situations, as it opens a door that can not be closed without implying a very insulting cut.