I know with Android that companies like Verizon install a "super cookie" that cannot be removed without rooting the device. Does anyone know if this is the case with iOS as well?
The Verizon "supercookie" is an HTTP header they add to your traffic. They do it via deep packet inspection, not anything on the device, and it affects iOS as well. After they got caught doing this they added the option to opt out at the account level.
Many Android phones come preloaded with carrier software, yes, and this isn't the case on iPhone. But I'm not sure if this is the "super cookie" you're talking about.