There's actually a reason for that... you had to physically be there to activate a launch, so just having the code means fuck all really.
If the generals are aware of the code being all zeroes, then that removes having the president and secretary of defense being required to order a launch. Which removes the whole point of having a military aide follow the president everywhere with the nuclear football handcuffed to his arm.
You have all this security to make sure that one person or just a few crazy people can't cause a nuclear war, but then one day that aide has to open the briefcase and say "zero..zero..zero...zero.....zero..zero..zero..zero" and he'll probably kill himself out of spite.