In regard to God's purpose, I do not think, generally, that mankind has had a grand enough vision. In my opinion, we tend to concentrate on God's transcendence in understanding such and bypass his associativeness (despite the well developed doctrine of the Trinity). The result has been, it seems to me, a reliance on form to define our relationship with God instead of the experience of relationship. When emphasis is placed on form, which is the very essence of covenant and the backbone of dispensation, distance from God is baked in the cake of our conception of our relationship with him. Jesus, in his high priestly prayer, revealed that he has something much more than that in mind for us.
I do not believe that Covenantalism or Dispensationalism adequately capture the overarching message of the Bible or provide a sufficient framework to order theology. Either misses that intimacy and faith color everything. Covenants establish relationship between two parties at arms length on the basis of boundaries for acceptable action by the participants. Dispensations seem scarcely different to me than a series of laboratory experiments performed on lab rats.
It is not that there are not aspects to either approach that recommend them to the student of God and his Word. Either, however, leaves the student who can't see past them dawdling, waxing cars for Mr. Miyagi, without a true apprehension of what is ultimately in the master's mind. From a practical standpoint, unregenerate sinners could never have confidence in their standing with God apart from a covenant, and prophesy is a muddle without seeing Israel in a dispensational sense. But God is aiming for more than sinners daring to come out from behind the bushes or for folks to get a history lesson from God's timeless perspective.
What, then, is the purpose of the covenant? Is it not merely an agreement with sinners that God will declare them righteous and make them new if they'll turn to him and put their trust in Christ? After one has come to that point then what? That is where covenant ceases and purpose must take over. It has never been God's purpose to leave sinners as sinners (but at least on friendly terms), and it certainly isn't his purpose to wait until the Rapture to get on with his purpose.
Covenant as the framework for understanding the overarching message of scripture falls short of the purpose of God. A covenant may give a sinner comfort, but God isn't aiming at sinners' comfort--his purpose is transformation. Dispensations are no better a framework: at best they are merely mile markers along the road of progress to God's purpose. God has made mankind to walk in eternal fellowship with him, a meeting of mind and spirit. That purpose is what gives all of the Word and theology cohesive structure.