Thanks to the wonderful folks behind the Reformational Publishing Project, I've been reading S.G. DeGraaf's four-volume work, Promise and Deliverance, an extended overview of the biblical story with a particular focus on the themes of the covenant and the plan of redemption. DeGraaf makes the case for the significance of the covenant early on in the first volume:

We must never lose sight of the great significance of the covenant. Without covenant, there is no religion, no conscious fellowship between man and God, no exchange of love and faithfulness. Without the covenant, man would just be an instrument in God's hand. When God created man, He had more than an instrument in mind: He made a creature that could respond to Him. Only if man was capable of responding would he be able to assume his position as partner in a covenant. Without a covenant, God would have only claims and man only obligations. But as soon as God gave man a promise, man also had a claim on God, namely, to hold God to that promise. And God then had an obligation toward man, namely, to fulfill that promise. Once the promise is given, we can speak of a covenant, for a covenant, after all, is an agreement between two parties in which the claims and obligations are spelled out. Of course we must never forget that the covenant was initiated by God and that God's promise elevated man to the rank of covenant partner.

Many different problems arise when the Bible is read without the framework of the covenant in place. We simply cannot understand our relationship to God apart from the covenant.