Tim Keller in introducing his book, “Prayer: Experiencing Awe and Intimacy with God” writes:

… these two kinds of prayer are neither opposites nor even discrete categories. Adoring God is shot through with supplication. To praise God is to pray “hallowed be thy name,” to ask him to show the world his glory so that all would honour him as God. Yet just as adoration contains supplication, so seeking God’s kingdom must include prayer to know God himself. The Westminster Shorter Catechism tells us that our purpose is to “glorify God and enjoy him forever.” In this famous sentence we see reflected both kingdom-prayer and communion-prayer. (p.4)

So prayer should be both for God’s glory and our good. Keller adds:

Those two things – glorifying God and enjoying God- do not always coincide in this life, but in the end they must be be the same thing. We may pray for the coming of God’s kingdom, but if we don’t enjoy God supremely with all our being, we are not truly honouring him as Lord. (p.4)

That last sentence indeed stems from John Piper’s thought and writing. We cannot glorify God, even if we are praying, if we don’t enjoy him.