The traditional deep littler method was on a dirt floor, as one person already mentioned.
The litter actually composted in the coop, generating warmth, and insects could live in the composting litter, providing fun scratching and a protein source for the chickens. New litter was added on top of the old litter.
The thing is, in order for litter to compost, there needs to be moisture in the bedding. Bone dry litter will not rot. On a dirt floor, that composting could occur beginning on the surface of the dirt floor due to moisture coming up from the ground, and work its way up.
A lot of people seem to be using something they also call a 'deep litter' method, but all it involves is deep litter, no composting. The floor is not dirt, and the litter is kept dry, and new litter is added to the old.
My personal preference is for a moderately deep litter - say 5-6", but I don't like to keep piling on new shavings for too long, because when you finally do clean the whole thing out, it's a real pain, there is so much litter in the coop. Also, I have asthma, and I find that things do get dusty when the old litter is left in, even when you add new litter on top. The pulverized poo etc. is still in the coop creating dust (ick.)