So then to create the scenario causing this glitch: you have an old device that tops out at IOS 6 attached to an account that is shared across more modern devices. The account was set at registration key when setting up the IOS 6 device years ago. The account was set at two factor when attaching to the modern devices.
Now when trying to login to account on IOS 6 device it still asks for registration key. The Safari on IOS 6 can't even successfully load the Apple account page (it stays blank) so you can't request a key from the actual device. So you go to the more modern device and load the Apple account page but it doesn't have the option to send a registration key.
I just made a new account completely for the iOS 6 device with a new gmail account, which got me in, then logged into the AppStore using the original account. In that case it had me add the two factor verification code to the end of the password when logging into the AppStore... an interesting workaround but it worked.