This isn't merely a game of hide and seek, but a means to refine our spiritual essence so that we can withstand the actual experience of HaShem without veils in the world to come.
Just as HaShem clothes Himself in the world, we clothe ourselves in the mitzwoth and in the Torah.
The Noam Elimelech teaches (parashath Hukath) that through focused Torah learning with great mesirut nefesh, self-sacrifice, the Tzaddikim can clothe their desires in the words of the Torah and in this way convince (figuratively) HaShem to fulfill their will.
There is nothing in this world that is not or cannot be clothed in Torah, he goes on to explain, and it is only through clothing something in the Torah through great self-sacrifice that HaShem will grant the will of the Tzaddikim.
Rav Morgenstern in Dei Hochmah l'Nafshech on Bshalach explains how mesirut nefesh (raising up mayin nukvin) is a necesary part of bringing down the divine influx of blessing to us. He goes into how tzaddikim can awaken people to mesirut nefesh.
It occurred to me this morning that when we don't do our part and awaken ourselves to HaShem through self-sacrifice, when we go to the Tzaddikim, we place an additional burden on them, that they must perform the self-sacrifice rather than us.. Which made me realize how much I need to sacrifice myself to the service of HaShem, bear my own weight.
Even if we aren't Tzaddikim, it appears to me that if we clothe our desires in Torah, Tefillah, Tzeddakah and Teshuvah we too can attain HaShem's will, at least when our wants coincide with His. So we should certainly be using Torah as the clothing for all of our Holy desires in all of our prayers.