Mail would be quarentined, and ways would be figured out how to screen potentially contaiminated from uncontaminated mail.
At that point the treat would be over, nothing would be "overstretched and open to attack." Again summarizing, rather than the mail delivery system continuing to operate until a time that things are stretched thin, the mail system would quickly shut down. The stretched thin so that the terrorists could pick their optimal time, would never happen. That is why the theory is flawed