Because, IMO, their disappearance after a friend (JA?) testified they had been in the foyer the day before NC disappeared, along with BC's washing the foyer floor that day, bolstered the theory that NC had been murdered in the foyer.
The ducks and sticks needed to disappear because they were either vomited upon by NC during her murder, or they were somehow damaged during the strife.
In turn, the vomit theory supports the idea that NC was killed soon after she arrived home, and since he was the only one there capable of killing her, BC did it. The autopsy report showed, IIRC, that she had only a small amount of red fluid and a small piece of onion in her stomach.
BC's mother found the ducks packed in a box, after NC's body had been discovered, IIRC. This does not mean that BC did not hide the ducks after something happened to them, and then put them in the box himself after NC went missing. There is no proof of that, however. The missing sticks were never found.
The trouble with the theory is that there is no proof, particularly beyond a reasonable doubt, that it is the truth. IMO, a theory is a lovely thing if it has evidence to back it up.