Legally children under 13 are not supposed to be unattended. This is not a criminal law, but from precedents in family law both the venue and the parent have civil liability if any harm comes to or from the child.

Since the venue has deeper pockets, even if the parent was 99% at fault, the venue could face 100% of the actual and punitive liability for any harm to or from the child. For example if your child ran into a elderly women and she fell and broke her hip - the venue could be liable for 100% of her medical costs.

If you child pulled a display down and hurt himself, YOU could sue the venue (and many parents would) even though you where mostly at fault.

There are millions more lawyers then pedophiles, and corporations need to protect themselves from these predators (the lawyers).