I think another variable is having more than one person with whom the child is attached to. The book mentions how a child with a relationship with a caregiver who is attentive and responsive will expect all future relationships to be similarly gratifying. I believe that a child will have this expectation for the second person he/she meets but will need to have it reinforced by having this same result multiple times with people he/she meets. For example if a child had a good experience with their mother but a bad one when her aunt babysits then the child may not be as responsive to their next caregiver.
I believe that this variable, while definitely a valid concern, cannot fully encompass the subtle nuances that exist in children of one parent or of families without large extended families.