Yes, why pray, is a very important question. For any difficult question like this one is, it is always helpful to recollect about the life of man-Jesus (anthropos-Jesus).
No question that many verses in the Bible proved that Jesus, the Creator God in Genesis and the Logos in the gospel according to John, prayed. In fact, he even prayed the whole night, as in, “And it came to pass in those days, that he went out into a mountain to pray, and continued all night in prayer to God.” (Luke 6:12).
Still, it begs the question, why pray?
This brings me to how you and I communicate. We use our physical senses of sight, hearing, feeling, gesturing, etc…albeit “material methods” of communicating. Without communication, how else can we understand each other? How can we learn or be guided by each other? Yet, this is a way to communicate with the “material world”.
How about the “spiritual realm”? Can we communicate with the “spirit” using “material or physical tools” like eyes, ears, etc? How could we be “on line” in a physical sense as in World Wide Web, unless we access the internet to learn, email, etc.? Similarly, the spirit-God, cannot be accessed except through spiritual means or venue. This is why we need to “pray”. It is a vehicle to communicate spiritually to a “Spirit-Being”.
Regarding, why pray when we “cannot change God’s mind”? Actually, God can “change or modify” his will, but within his limits of perfect judgment. Didn’t he delay the destruction of Nineveh, “haggled” with Abraham as to how many “just people” needed to save Sodom & Gomorrah? How about Adam in the garden of Eden? He did not like Adam to eat the fruit of knowledge of good and evil and he could have “forced” Adam to follow. Yet, He did not because His perfect judgment allows Adam to “freely choose”.
Remember, God said, “…not like the covenant which I made with their fathers in the day I took them by the hand to bring them out of the land of Egypt, My covenant which they broke, although I was a husband to them,” declares the LORD. But this is the covenant which I will make with the house of Israel after those days,” declares the LORD, “I will put My law within them and on their heart I will write it; and I will be their God, and they shall be My people. They will not teach again, each man his neighbor and each man his brother, saying, ‘Know the LORD,’ for they will all know Me, from the least of them to the greatest of them,” declares the LORD, “for I will forgive their iniquity, and their sin I will remember no more”(Jer. 31:32-34; Heb. 8:10)
Yes, the promised Holy Spirit by the Father to the Son, who sacrificed his life for remission of sins and subsequently for us to receive the Holy Spirit (John 16:7), is now available for in-dwelling and writing the “laws into our fleshly tables of our heart and mind” to empower us. The Holy Spirit working with the “spirit of man”(the “breath of life”), to nurture, guide, teach, direct, suggest, empower, seal us. Ultimately, prayer helps us develop the character through the Holy Spirit to be “one” with God in “wisdom”.