This is acknowledging that everything that we have is based on Hashem granting it. Every one has needs and desires that must be taken care of. It is appropriate to ask Hashem to help us understand which ones are appropriate and to help us merit the fulfillment of those desires. Note that Moshe Rabbeinu asked to be allowed to go into the land. In the story of Yishmael, the meforshim teach that a sick person's prayer for health is heeded more readily than someone elses prayer for that sick person. Rabbi Hayim Halevy Donin’s useful book points out the Talmud mentions eleven sages and the supplications that each customarily added to the Shemoneh Esrei (Berakhot 16b-17a). The prayer of Mar, son of Rabina, a fourth-century rabbi, became a favorite and found its way into the prayer book at the end of the Amidah. Thus, the powerful ending of our current silent devotions began as one of many personal prayers.
Rav Kook: Prayer at Sunrise points out
The Sages instituted a fixed text for prayer, so that all would be
able to pray eloquently and for appropriate objectives. Yet the Sages
also warned against prayer that is keva - literally 'fixed' or 'set.'
What exactly is this keva prayer that one should avoid?
The Talmud quotes a number of explanations. The simplest definition is
that keva is a prayer consisting solely of the prescribed text,
without any personal or individual requests. Others explain keva to
mean a dry, sterile prayer, lacking heartfelt petitions.
This article discusses the matter in modern times but is too long to summarize.
I can't guarantee what will happen if you use prayer and tzedakah to
ask God for help. But you just might create an unstoppable flow of
healing and repair, a very different result than if you close your
heart and do nothing. You just might open up a path of light where
before there was darkness.
Leonard Felder, Ph.D., is a licensed psychologist whose most recent
book is Seven Prayers That Can Change Your Life: How to Use Jewish
Spiritual Wisdom for Enhancing Your Health, Relationships, and Daily
Effectiveness (Andrews-McMeel, 2001).