This is just a placeholder answer while look for the complete connection to the phrase "cheaper by the dozen".
We know that englishmen in the colonies and what would become the "United States" forced prisoners of war (what englishmen refer to as "slaves") to have sexual intercourse with their mothers, in an effort to produce more prisoners of war, for free labor, fun, glory, material gain, and experimentation, see Medical Apartheid The Dark History of Medical Experimentation on Black Americans from Colonial Times to the Present by Harriet A. Washington. Forcing young prisoners of war to impregnate their mothers is but one of the horrendous practices of englishmen in the western hemisphere. Without such experiments what is referred to "modern medicine" would not exist. If you find the time, browse the historical medical records of the University of Chicago.
That is the origin of the term motherfucker from which the cheaper by the dozen phrase was used to refer to the offspring of such forced impregnation.
The late Dick Gregory revealed many of these historical facts before their passing. It has been some time since last reviewed the actual phrases usage. Am not entirely certain if Dick Gregory is the one and only source of the meaning of that phrase, within the context of the offspring of male prisoners of war in the western hemisphere being forced to impregnate their mothers to produce more prisoners of war.
It is not surprising that anglophiles deny, or refute such origins of terms in the english language.
Though for an individual who is not an englophile, it is common knowledge that english is first and foremost an equivocal language, intended to be used for deception, capable of having more than one meaning for each word or phrase. There is no such thing as "good" or "proper" english. The language is a result of conquest by the Normans, Romans, whores, convicts, pimps, murderers, imperialism and several hundred years of institutional white supremacy.
In any event, this Dick Gregory - On Slavery, Reparations and Hurricanes
... we can't have no more. How we gonna do this?... So he made me, 14 years old, put a sock over my head, and have sex, fuck my mama...
...cause she didn't want him to get made and start killing the slaves...
... and so, I had to screw my mama man...
... That's where the word motherfucker comes from and then white boys shit and they hated the word until they got around black folks...
... and now you go to a white movie and they say mothafucka before they finish running the credits from the movie...
is a brief introduction to the emergence of the phrase "cheaper by the dozen" being used to refer to the offspring of so-called "black" or african women in the western hemisphere being force to be impregnated by their sons, the result of which was often birth defects, which were still valuable "property" for those englishmen who bought and sold human beings. The interview provides accounts for the origin of the terms honky and motherfucker. Will edit the answer to address specifically how the motherfucker history resulted in cheaper by the dozen.
Note, that same interview describes the origin of the term honky, which is derived from english, or so-called "white" men literally honking the horn of their vehicle outside of the whorehouse they were visiting to buy sex from so-called "black" women.
