Presumably, the "security" does not come from the assumption that the serial numbers are private information -- it comes from the assumption that you can only reprogram the parts with top-secret Apple internal tools. There's no reason the serial numbers need to be paired per device; iOS should be able to check any serial number to see if it is genuine Apple. Much like you can go to https://checkcoverage.apple.com and check the warranty status of the whole iPhone based on its serial number.