I think your analysis is a bit heavy-handed. Most people have a common understanding of this word. Referring to a woman as "this chick" is obviously a tone that lacks respect and most American males understand the subtle differences in connotation between "chick" and "dude". Yes, they are mostly interchangeable but in certain contexts the word "chick" can carry a somewhat dismissive tone with a little more intensity than the word "dude" and this is just a subtlety of the language that is not easy to articulate.

Women in positions of authority or power are generally not referred to as chicks, it's hard to come up with a universal rule, but if one considers female authority figures throughout one's life it becomes easier to see where "chick" is usually not acceptable term for a woman you respect whereas "dude" has a more neutral connotation for male authority figures, e.g. in reference to a strict male authority figure "that dude is a hardass" or "that dude will knock you out".