Drawdown occurs when the air cell changes shape as the embryo, using the egg tooth, punctures the inner shell membrane and enters the air cell. The egg is designed to allow ease of exit from the egg, and the egg tooth is used to begin unzipping the eggshell in a circular manner, usually at the larger end of the egg.
The initiation of hatch occurs partially from the increased carbon dioxide level in the egg. This causes the embryo to begin twitching it's muscles, allowing the inner shell membrane to be punctured by the egg tooth. The chick then begins breathing the air in the air cell. As the carbon dioxide level begins to rise again, the muscularis complexus (the pipping muscle) at the back of the neck begins twitching again, facilitating the hatch. Abdominal muscles also begin twitching, which helps draw the yolk sac into the coelom. Leg muscle twitching helps strengthen the legs.
Assisting the hatch is a difficult decision, and in this author's experience, many aviculturists will do more harm than good by assisting the hatch. Normally the chick will hatch 24-48 hours after drawdown has occurred. By making a pin-hole in the egg shell over the air cell, the carbon dioxide level will drop, actually slowing the hatch. Making a pin-hole or opening the air cell end of the egg should only be done if the vocalization level of the hatching chick is decreasing or other signs indicating that the chick is in trouble are evident (for example, if the chick doe not pip into the air cell).
Also remember that unlike a mammal, a chick can go three days without food or water, and there is air in a pipped egg, so staying in the shell is not dangerous in the same way that a mammal staying too long in a uterus can be.
Bird embryo's are not supported by placentas as mammals are. Instead there is a network of blood vessels that line the shell and ends up in an umbilical cord that is attacted to the quail at it's "belly button".
When the quail is ready to hatch, it breaks into the air cell and begins to breathe. This triggers the network of supporting blood vessels to begin to shut down. All the blood from these vessels must drain into the quail before it is ready to hatch.
The quail struggles and movement helps this process and by the time it is ready to hatch there is no more blood in the vessels that line the shell.
If the shell is broken before this network of blood vessels has stopped functioning and one or more of these vessels is damaged, there will be bleeding. Baby birds don't have a lot of spare blood and this can be dangerious.
When a mammal is born, the umbilical cord is usually crushed before the baby is born, so it does not bleed. During a caesarean section, the cord is clamped before cutting for the same reason.
It's simply not possable to clamp the cord of a baby bird before breaking the shell, so opening the egg while that network of blood vessels is still functioning will cause many to be torn which would be the same as tearing open (or removing) the placenta while the baby is still using it. The baby will bleed to death.