Tillering, by its very nature, is done to expose flaws in the way a bow is bending. These flaws are made up of places where the bow is bending relatively too much or too little. Those flaws can lead to damage of the structure of the wood if the bow-to-be is bent for too long or too far with the flaw present.
A pulley system allows you to watch a bow bending just small amounts for short periods of time, leading to less damage of the structure of the wood.
Alternatively, systems where you pull a bow-to-be to a certain draw length and hold it there while you evaluate it exacerbate the damage by bending those flaws longer than necessary.
Ideally, we would cut the bow out and it would be perfectly tillered and at the exact draw weight we want before it bends at all. Since we function in reality though we have to minimize the negatives of our process.