Why do people consistently insist on calling it 'ego'?

"Ego" in the Freudian sense of "I, myself" comes from philosophy (metaphysics), dating from the late 1700s.

"Ego" in the way people use it in the vernacular, meaning "conceit" is a later permutation.

"Ego" is also used in the vernacular to mean something closer to "id", that is, "unrestricted human desire". That sense comes from Eastern philosophy, as in "One must destroy the ego in order to attain enlightenment." That doesn't mean destroy the organizing principle of your personality (Freud) or stop thinking well of yourself (conceited). It's a separate concept, and it got translated with the same word.

So the three senses are all correct, they are just easy to confuse, and which one someone intends is a matter of context.

Yes, I understand the difference between the id, the ego, and the superego. I also understand what people generally mean when they use the term ego. Not everyone has studied psychology, you know.

If you check a dictionary you will find there are several definitions for "ego" alongside the psychoanalytic one.

Id, ego, and super-ego are the three parts of the psychic apparatus defined in Sigmund Freud's structural model of the psyche; they are the three theoretical constructs in terms of whose activity and interaction mental life is described. According to this model of the psyche, the id is the set of uncoordinated instinctual trends; the ego is the organised, realistic part; and the super-ego plays the critical and moralising role

Most actually do not or have forgotten it. Trying to change an idiom is probably a lost cause anyways dude.