I have to say that the automation that you unlock later is complete ass. For example, I wanted to make a breeding system that takes whatever males slaves get born and immediately shunt them into a butchery, with a separate flow for females that shunts them into a gloryhole, that then leads to a butchery. So I decided to test it with a new slave intake > slave room > butchery.
The problem is that you can't immediately just slaughter the males. They can only go from a slave pen into a breeding room and then into a butchery, which means that each one needs to die from getting fucked by a max depravity woman, an oni female that has a "reduce health for partner" debuff (buff in this case), or preferably both.
The problem with this is that it can't keep up with the influx. And that's for something relatively simple like new slave traffic. Good luck replacing that system with a growth room in place of a new slave cage, as the breeding automation loop simply doesn't work.
From what I can tell, the intended loop is Slave cage > breeding room > delivery room (babies are shunted to a growth room) > milking room > slave cage which is fine in theory. The problem is that milk is almost always at a surplus once the system is automated, which means that whatever females you have in the loop will be stuck in the milking room when you reach your maximum milk storage. And if you have more than 4 girls in said loop, any girls after that will be shunted to the growth room, which might be fine, except there's no way to disallow it, or the aforementioned milking. Which means constant micromanagement, which the automation system is supposedly there to solve.
Edit: And I completely forgot to mention that the automation system doesn't check what slot in another room is empty. In the case of a breeding room that has no male in it, but does have a female, either a female or male can then enter that room, which can then completely freeze the flow if a woman tries to enter, because only one slave can move between a room at a time, so the female will just sit there blocking it.