What everyone else already said. I have heard of people accidentally breaking the egg late in incubation and the chick being fine, but usually it's quite dangerous because the baby can easily bleed to death and/or the yolk can dry up before it has been completely re-absorbed.
It's actually quite similar to what happens in humans in the very rare case of a "placenta previa," or when during a C-section the doctor accidentally nicks the placenta with surgical tools (much more common than placenta previa--in humans as in chicks, most of the time it's best to let well enough alone already! lol). In either case, the placenta is still full of blood and is still connected to the baby's blood stream, so when it starts to bleed, the baby can quickly bleed to death. (Placenta previa is when the placenta partially covers the cervix so in order to be born, the baby has to push through the placenta which tears it and can cause both mother & baby to bleed to death--like I said, EXTREMELY rare, so no worries for any new moms-to-be out there, lol).
In the case of a chick, by the time it is ready to hatch, it is essentially completely surrounded by its "placenta." In order to hatch, it has to cut off the blood supply to the "placenta" so that it won't bleed to death. The way it does that is that it turns in the shell and gradually punches a line around the shell, which also punches those blood vessels shut. Then it rests, absorbs the rest of its yolk, and then pushes its way out. That is why it takes so long from pip to hatch.
And it's also why you can't just crack an egg open and expect the baby to be fine any more than you can just rip a baby & its placenta out by C-section without some pretty nifty hand-work by a skilled doctor (obviously that's necessary to preserve the mother's life too, but I'm just sayin'--the baby would die too if the doctor weren't working pretty hard to prevent it).