“Why did we substitute the word “Citizen” for that of the more familiar word “Subject”?”
Because we switched our form of government from a feudal monarchy or a parliamentary monarchy in which a monarch was the sovereign reigning over the subjects, which included the freemen citizens, to a republic in which the sovereign was the body of freemen citizens of the municipalities, states, and North American confederation.
So the concept of "citizen" does not stem from English common law. That is my point.