That's a good point. That is what I meant by "and config" in my first sentence.

IIUC if the keypair was a certificate with a few other fields foreign networks could give you some basic communication with your provider and decided if you should be allowed to use this network and if/how to tunnel you back to the home network.

But the main point is that it should just be data that the user can port around to different devices as they see fit and that they can trust not to do malicious things.