I once heard the following explanation:
The word to pray is להתפלל, which is the passive reflexive of פלל, judge. So להתפלל means to cause one's self to be judged. The purpose of prayer is to put yourself before Hashem and test how sincerely you see Him as the source of your needs.
So, indeed, the prayer is not "for" Hashem, nor is it to make sure He knows what you need. It is for yourself.
In response to edited form of question:
This would still require performing the act of davening, just like in any Mitzvah with a given purpose, you still have to do the action. If you were to know the "message" of lulav, you would still have to take the lulav and not just meditate on the message. This is true of all mitzvos1. There are a number of explanations for why this is true, but Sefer HaChinuch explains this to be because it is through the actions that we internalize the message of mitzvos, and the same would apply for this mitzva as well - in order to make it real to ourselves that we are standing before Hashem, we have to actually do it.
Nefesh HaChaim discusses this point explicitly, specifically regarding davening - the mitzvah of davening is fulfilled only through the speech aspect of it, and yet it is called עבודה שבלב, service of the heart. Just like in every mitzvah the mitzvah is only fulfilled through the action of the mitzvah, so to in davening the fulfillment of the mitzvah is through the action, even though the "idea" of davening is focused in the heart.
End of 2:1
מנם כל עיקר ענין טהרת הלב. היא רק למצוה ולא לעכובא גם לענין התפלה אף שנקראת עבודה שבלב כמו שנתבאר קצת לעיל סוף ש"א שהעיקר בכל המצות היא המעשה
End of 2:14
הגהה: והגם שהלכה פסוקה בש"ס שתפלה נאמרת בכל לשון. היינו לצאת ידי מצות תפלה כמו שנתבאר לעיל סוף ש"א שבכל המצות ואפי' מצות תפלה שנקראת עבודה שבלב. עכ"ז עיקרן לעכובא הוא חלק המעשי שבהן. אמנם למצוה מן המובחר ודאי צריך לצרף גם טוהר המחשבה וכוונה שלימה.
1One could ask the same question about any mitzvah - "If I shake a Lulav and don't think about it at all, I have fulfilled the mitzvah, but if I think about every message and lesson involved in the mitzvah and don't do it, I haven't fulfilled the mitzvah. So what is so inherently special about shaking a palm frond?" The act of the mitzvah may be the basic framework of the mitzvah, but the intent put into the action is what directs that action and gives it meaning. See Nefesh HaChaim quoted later on in this answer.