What Is The Point Of Prayer?

[Sword of Christ]

Intercessory prayer is a request to God or Jesus to change his mind about the already established plan for the universe and make it go another way.

Oooh now that's a freewill killer right there. No our lives aren't mapped out because we have right here some degree of independence from God. I think it's somewhat vital that we have freewill and there is no way atheism or naturalism would allow us to have it (chemical reaction, neurons, instincts, programming etc). Neither would deterministic theism. The central theme of the Bible as a whole is that we are independent beings with our own independent will but with a morality grounded in God. As for Gods relationship with time I'd recommend reading Lane Craigs book Time and Eternity, God essentially exists in relationship to time as we do while the universe exists. Though can still exist without the universe and exist beyond time. So there is no preset plan for our lives individually and if there were then any change he would make would have been part of the plan anyway.

Of course, this implies that a perfect deity's plans, which would (by definition) have to be perfect, should now be altered at the urging of an imperfect being. This is logical reason enough to refute the possibility of intercessory prayer's effect

It would be logical but then I rejected your premise that God sets everything in our future out ahead of time so this is a moot point.

because perfect beings cannot be outguessed by fallible mortals. Nevertheless, believers in the power of gods, saints, and angels claim that these agents are able to alter or suspend the well-established laws of the universe at their whim or at the request of the believer, through prayer.

The function of miracles would just be an extension of the natural laws as defined by God as it exists. Nothing would be suspended or violated. We don't get to say what can and can't happen we get to understand the natural order of the universe with our God given reason and understand the nature of God thorough our personal experience and the revelation he has seen fit to give us, in the Bible and the gospels. Everything you need to know right there (that isn't specifically scientific but we can cover those details ourselves)

If we were speaking of magic or sorcery, or any belief systems outside of Western Judeo-Christian tradition, most would agree that these ideas (of intercessory prayer's effectiveness) are ridiculous and consist of superstition at best.

There is a magic branch within the Judeo-Christian tradition. This is when you get into alchemy and that kind of thing, something Issac Newton was into. I suppose you could call it the "Western Esoteric Tradition", I have a bit of an interest in it myself.

In only one area, the field of Judeo-Christian theology, are the very same phantasms accorded the status of legitimate entity. Why? Why are Judeo-Christian superstitions by any accepted taxonomy of logic allowed to maintain a grip on, not only political, social and economic values in our society, but on scientific ones as well?

Because it is true and of real value to human life, society and culture one way or another. This is God we're talking about here, the ultimate be all and end all. Luminous beings are we not this crude matter.