Re: better get a mobe, then.
> As opposed to SMS
Since the iPad and iPod touch I specifically mentioned cannot receive SMS, sending one wouldn't be applicable anyway would it? Duh! Therefore SMS is not even an option for many iOS users (the very people most likely to have an AppleID in the first place).
> SMS is an incredibly stupid choice. You specifically need a mobe, it spends several minutes -sometimes hours- wandering around the network before it reaches the end user
What? You need to change your network provider if SMSs take "several minutes -sometimes hours" to reach you, unless New Years Eve is celebrated daily on the planet you're from. Several seconds - at most - on any of the 5 networks I've ever used.
> Push messages on the very device from which you are trying to recover your password
If you don't care enough about your personal data to protect the device with a passcode then someone getting access to your AppleID probably wouldn't worry you much either.
> it would be trivial to mount an automated hacking procedure just by running ~10 lines of code at any step of the transmission (including, but not limited to, the recipient's handset)
Trivial? LOL. You have absolutely no idea what you're talking about do you? Finding and exploiting a vulnerability in Apple's systems, the mobile network providers systems, or the handset OS allowing you to run that "~10 lines of code" would not be trivial. Nor would setting up some 'man-in-the-middle' attack.
Certainly not impossible, but certainly not trivial either, and definitely not requiring just 10 lines of code to pull off.