Plus, some of the science (such as it is.. the science is not very definitive) of why 5-6ppm is the optimal upper amount for the phase prior to the nitrite spike (what I like to call phase 1) is really quite interesting (if you like that sort of stuff)... When the level gets to around 8ppm it encourages a different species (different from the one we want) to outcompete and later, this imposter species can't sustain itself, dies off and must then be slowly replaced by the species that we ultimately want.
The reason not to go lower, down below 4 is exactly as oldman says, you want your ammonia oxidizing population to be big enough to handle the fish load you plan to stock in the tank.
~~waterdrop~~
ps. (hope I've got that science right, it was probably from the TFF science section somewhere..)