Question: Why aren't animals stunned first before they are ritually slaughtered?
Answer: The laws of kosher slaughter (shechita) are designed to be the most humane possible, preventing pain to living creatures (tza'ar ba'alei hayim), by a swift and immediate death.
If a kosher slaughterer (shochet) uses a properly honed and sized knife for the animal in question (generally twice as long as the diameter of the neck of the animal) and the knife severs with one motion the trachea, esophagus, and blood vessels of the neck, then suffering should be minimized. Properly executed and with the most modern equipment devised to protect against violations of the fundamental laws of kosher slaughter, shechita will result in the animal dying within literally seconds and then bleeding out maximally.
What we don't want to do, obviously, is to frighten, mishandle, or cause the animal to struggle, for that would lead to emotional pain (tza'ar) and it might also lead to defective slaughter (which would then be pointless if the animal were not to be kosher meat). While shechita isn't foolproof, it has been observed that the animals suffer as minimally as possible when slaughter is done by trained and experienced shochtim. Minimal suffering is the goal no less than a pronouncement that the meat is kosher for not having violated the physical steps of shechita.
According to Rabbi Isaac Klein z"l of the Conservative Movement, there has been discussion about stunning, by electricity or anesthesia, for a number of years. Some have seen no objection to it, but the overwhelming majority have ruled against it.
In my own limited experience, the use of a stun gun or a bullet frequently doesn't actually stun or kill the animal; it actually can add to the animal's pain and thrashing. Thus, stunning techniques aren't guaranteed to reduce animal suffering.
In my opinion, the best way to further reduce suffering is newly designed equipment that facilitates an upright shechita. It literally cradles the animal, prevents the head from falling, and thus makes it unnecessary to invert the animal. I understand that many Orthodox authorities have not yet approved this new implementation, and it is going to be expensive for the slaughter houses to do so. But I believe that if the resulting meat is as kosher physically and it is obtained in a more humane fashion, then we should buy kosher meat from slaughter houses that use this new equipment.
I should add that recent films, study of the issue and a study of health rules for the human being are urging me to consider a far more vegetarian way of life. I already overwhelmingly eat fowl rather than beef. Rabbi Klein notes that perhaps all of these regulations for kashrut were intended to promote a vegetarian lifestyle. He suggests that perhaps God permitted us to eat meat as a concession to our humanity, but that vegetarianism is really God's first choice.