In order to delete an Apple ID, you first must have access to the device that is associated with it. Then you have to get an activation code through Apple’s website from that device through the network, and submit a form and wait up to 7 days, during which time they retain the right to refuse your deletion request based on no particularly detailed policy. Once you have verified that your account is deleted from the device, you may no longer log in with your Apple ID to wipe the device. Catch 22. Apple pwnz u.
Moral of the story: remove your device from the account before requesting account deletion, then log out of your Apple device and “trust” Apple to delete your account.