I do not know much about the court system or anything in New York, my experience is in a different state. However, in my experience, if CPS would have petitioned the court in any of the three instances, the petition would have been denied. Before removing a child, unless there is a risk of immediate danger, you are supposed to provide the family with services or give them a chance to clean up a dirty house. To go into court and say that the family did clean up when asked and the child, as well as everyone else, deny any problems, the court will throw it out and ream out the worker for filing the petition.
Even if a petition was authorized, there is no way the child would be in the system for any length of time. All the parents' attorney has to do is demonstrate that the house is clean and, since the child denies any problems, the child would be returned home.
As a worker, you can have a gut feeling, and you can know deep down that something is wrong. However, the court doesn't let you get by with gut feelings, you have to have hard evidence that the parents are not cooperating and being at home is detrimental to the child. If a child is well adjusted, saying they are eating, saying there are no problems, there is adequate food in the home, and the parents follow directions to clean up, there is no LEGAL basis to remove the child.
Sometimes it sucks being a social worker because sometimes you are forced to do something you don't feel in your gut is right simply because of the law/court. Yet, when something happens, the social workers are the ones that get "thrown under the bus" so to speak.
As I said, I cannot say how New York works, I only know from my experience in a different state. There is so much that factors into social workers decisions that people don't realize and don't know about. I will admit, there are bad social workers who make bad decisions. But that's not always the case. And before someone brings up that they never brought any of the allegations to court, so how would they know how it would be handled, let me say this. If you've worked in a specific county for any length of time, you learn what flies and what doesn't. You know exactly what needs to be in the petition and what proof you need. If you don't have that proof, you know to not even take the case to court.