Flatbusher, are you a master of Chassidus and Kabbalah that you can say that with such authority?
The fact that it doesn’t completely absolve one of his sins is undisputed, but to therefore claim it has no utility whatsoever is an unfounded stretch.
If I had to put a rational spin on it, I would say that the fact that we acknowledge that we deserve the chicken’s fate is itself a form of viduy and brings hirhurei teshuvah. I wouldn’t claim to know what deeper meaning it has, but won’t deny such a possibility out of ignorance.
Why would we make up our own definition of tzaar baalei chaim when there already are halachic parameters for it?
ZD, it says nefesh tachas nefesh right there in the machzor. Tzeddakah is a beautiful add on, and has become a part of the minhag, but who says the profits are not going to tzeddakah?