In the fifth Sandman collected edition; A game of you, The Cuckoo introduces themselves as an abandoned imaginary friend who took the form of Barbie's childhood. I want to know what the Cuckoo represents, or what kind of monster it is. Does it feed on insecurities of little girls or does it only require an over active imagination? Or does it thrive in the over active imaginations of children taking refuge from reality in their imaginations specifically? Maybe something completely differently that I missed?
Regarding the point:
Or does it thrive in the over active imaginations of children taking refuge from reality in their imaginations specifically?
The answer is a definite no. Gaiman had already explored the theme of a child taking refuge in dreams to escape an unbearable reality -- in the case of Jed Walker, in the stories collected in Sandman Volume 2: The Doll's House. A Game of You is doing something different.
The Cuckoo explicitly tells Barbie she had a happy childhood with loving (albeit somewhat boring) parents, and she is not subconsciously repressing any memories of abuse. Of course the Cuckoo is not to be trusted; but in this instance, we are given no reason to believe it is lying.
Does it feed on insecurities of little girls or does it only require an over active imagination?
We are told the Cuckoo lives inside little girls' dreams, so a propensity for vivid dreaming is likely to be the key.
Also worth noting, the Cuckoo would normally have matured and left its host much earlier, but stayed in place because of Barbie's connection to the skerry known as The Land.