Good post & most likely most (if not all) of this is correct.Hens are poor mathematicians. I know you have seen the term "chicken math" used here. Chicken math is no math or reason at all. So maybe to your hen two live chicks in X amount of time makes sense.
This will get me in a lot of hot water with some people on BYC but chickens only react, they don't think, and they don't reason.
A black hen with 11 white chicks and one black chick is liable to kill the only black chick that looks just like her because it's color is different from the 11 white chicks she just hatched. X The same is true for a white hen with 11 black chicks and only one white chick. Chickens just don't have a sense of self like humans do. We look in a mirror and see ourselves. Chickens who look in the mirror only see a strange new chicken whose place on the pecking order must be sorted out.
Chicken math caries with it the inability to tell time. Hens with new chicks under them get antsy to be about the business of feeding their new children, and Zeus help any chick that is not yet strong enough to follow her. Your hen, my hen, no ones hen comes equipped with an ultra sound machine to scope out un-pipped or pipping eggs. It is much preferable if you can confine the hen and her chicks inside her nest, and keep the nest inside a safe, quite, and very dark but cool place were she should be happy to hover her brood an extra 24 hours or until they are ready to come out into chicken society.
It is also fairly common for hens to kill first pipped chicks and I am going to lay it to the fact that hens don't come equipped with a stop watch or calender and that the hen sees the first chick as an intruder. If the hen is unable to see her brood until they all are hatched out and dry then chicken math kicks in because the hen then can't make heads or tails out of which chick is which. Which brings us full circle back to, why did my hen kill the only off color chick she hatched when it is the same color she is??? "Chickens only react, they don't think, and they don't reason." I already said that didn't I?
Most animals when they look in the mirror don't realize its themselves... eventually they just choose to ignore the "other" animal.
Maybe some do eventually realize (the smart ones) .
I personally think a hens reaction to any chick is just in the hens personality. You hear about mother hens with a wonderful temperment, prepared to lead her chicks through a storm so to speak, willing to brood over them constantly. Those hens put the chicks in the center of their lives, even be willing to encourage & attend to an individual chick that is not doing as well as its siblings because her instinct is so strong.
I wonder sometimes whether its because the hens are not understood properly & then have not got the personality there enough to cope with being mothers. As put above an animal doesn't usually think. Usually. Most reactions are purely influenced by emotion & instinctive reaction the same way as you & I have the first thought go through our heads when we see an image. The thought is different depending on the personality. A women who hates baby's may well look at an image of one & think "Egh, disgusting little thing" & her instinct & reaction is to either not look too hard at the image & ignore it or get rid of it in some way I.e walk away . Meanwhile a woman who loves babies will still go "Ahhh. How adorable" even if said baby is dribbling snot.
Any bird won't use its brain & be encouraged to develop a distinct personality unless it has been encouraged to when it was younger. I certainly was not even aware I would be able to get pregnant when I was older & it was never, ever something that was encouraged by my family. Maybe if my family had not constantly drilled into my head that babies were a dirty, unnecassary drain on women's lives & careers, finances & sleep, then perhaps today I would think differently.
A woman may well think a babies picture is horrible, but she would not voice her opinion to others because they do not understand why you feel that way. As one of those women its because I know I am expected to look at a baby and go "ga, ga" by society whether I want to or not. Yes, some babies are cute, but frankly I prefer raising animals without the 18 year toll. I just don't like kids, period.
If a hen is thinking along the same lines as I do, then without the logic of "I should not do it" the bird will reject & actually kill the babies because it does not know what else to do. It has gone broody purely out of instinct, not because it wants chicks. Even I went broody once when I temporarily came off birth control & it lasted 2 years (What the hell was I thinking!?!) during which I found out I thankfully A) couldn't get pregnant easily & B) nearly ruined my marriage with foolish thoughts & words directed at my husband out of frustration due to how I was feeling. Babies were suddenly everywhere & I suddenly wanted one more than anything else, I spent stupid amounts of money on ovulation tests, books, pregnancy tests & baby gear trying to conceive over that 2 year period. My poor husband was suddenly subjected to strict diets, the removal of his ciggarettes, limited exercises, pre-planned cold sex in one position 3 x for 1 week of the month & then forced to remain abstinent for the rest of the month, I suddenly was "ga,ga" at babies in the street, crying at baby adverts & mourning each period one after the other for reason I didn't understand because I would ask myself "Why did I want a baby so suddenly?" & I couldn't even answer myself. I knew deep down I didn't really want a baby. But did I? Didn't I? The confusion for me was horrible, God knows what it must feel like to a poor animal with less mind power.
To be honest, despite my massive attempts, if during that time I had actually fallen pregnant, I think I would be very depressed right now looking after a baby.
Then as fast as it happened it went away. I quite literally woke up one morning feeling more myself again & things just got better after that.

So maybe these hens are just hatching out eggs because of their instincts are telling them & then deciding after all they don't want chicks, they don't even like chicks & they don't know what to do with them. They get distressed & then because the chicks won't/can't leave, they kill them.
Nature can be very cruel.