Reason - if, in an accident, it is later established that the driver fitted the child seat incorrectly, or restrained the child incorrectly, or the restraint device was later found defective in any way, and the child is injured or killed, that driver is going to be hung out to dry.
On the other hand, if the accompanying adult provides the device, fits it to the vehicle and then retrains the child, then the driver can rightfully claim that the accompanying adult is responsible. In sue-crazy US of A it’s not worth taking any pointless risks.