It isn't that parents of single children infantilize them. They see their children as precious. They plan to have single children to give them the best opportunities whether it is educational, cultural, &/or socioeconomic. They want their children to be exposed to the best.
A few parents may be overprotective because they want to shield their children from negative elements which may disrepair their children. Parents of single children are involved in their lives because they CAN be. They have the emotional & psychological resources to give their children the individualized attention the latter need to thrive. It is common in single child families that there are 1:1 relationships & discussions between parents & children as there are no sibling interference nor competition.
Parents of large families are seldom, if ever, involved in their children's lives. For the most or all part, children in large families raise themselves &/or each other. Parents of large families let children to their own devices. The rule of large families is akin to the law of the jungle-children either swim or fall through the cracks.
Children who can successfully navigate their lives thrive while those who CAN'T oftentimes fall through the proverbial cracks. Parents of large families AREN'T there for their children- it is EACH child for himself/herself or each other. Parent-child relationships are next to non-existent in large families.
Parents of large families don't believe in communication w/their children, they leave that to the siblings. They DON'T view their children as precious since they have so many of them. Children of large families are de-individualized & viewed & treated as part of a group. Groupthink is common in the large family environment.
Since parents are uninvolved in their children's lives, they are pushed to be adults early. Children in large families assume adult responsibilities in childhood, from working part-time & weekend jobs to supplement family income to raising themselves & other siblings. Childhood is its strictest definition does not exist for children in large families. One can say that childhood is a luxury for children in large families, perhaps w/the exception of the youngest.