Well, that's the idea or the ideal, anyways. Unfortunately, incompetent investigators are too often prisoners of the conventional. They see a dead little girl and because statistics tell them that it's likely a family member is responsible, they stop looking anywhere else and miss clues that would point them in other directions.
Instead, they focus on the confession rather than the investigation. It happens all the time. It clearly happened here.
Also from the article I quoted: “The timing of the charges also seemed curious, coming just six days before a tight election for state’s attorney between Tomczak, the incumbent, and a bitter rival, James Glasgow. What’s more, Tomczak’s father, Donald, second-in-command at the City of Chicago’s water department, had just been named in a federal indictment for corruption.”