Would it make any difference in your understanding of the requirements of salvation if the Abrahamic covenant was omitted from the Scriptures?
There is no part of Scripture teaching that can be omitted without loss. However, God has arranged that His plan be stated in numerous ways. The same point is often revealed plainly and reinforced through literary devices such as allegory and simile.
When God said to Abraham, “In thee shall all families of the earth be blessed,” He was stating His long-range purpose for the earth and the salvation of worthy mortals. Ultimately all who live on the earth will be blessed by God. The same promise was stated by our Lord in the prayer He taught His disciples, “Thy kingdom come. Thy will be done in earth, as it is in heaven.” It was stated again in the promises to David and his seed regarding the kingdom of Israel: “My covenant I will not break, Nor alter the word that has gone out of My lips. Once I have sworn by My holiness; I will not lie to David: His seed shall endure forever, And his throne as the sun before Me” (Ps. 89:34-36). It was stated again by Isaiah when he wrote, “And all the ends of the earth shall see the salvation of our God” (Isa. 52:10). It was the promise of the angel concerning Jesus, that “the Lord God will give Him the throne of His father David. And He will reign over the house of Jacob forever, and of His kingdom there will be no end” (Luke 1:32-33).
But we must remember that a covenant is a two-sided arrangement. This is true also of the Abrahamic covenant. God commanded Abraham, “Walk before me, and be blameless” (Gen. 17:1). The same requirements rest upon all who would participate in the benefits of the covenant. Whatever God asks, we must be ready to do. It is a law of faith and obedience, whatever the specific commands from God may be. We must be ready to give up our thoughts for God’s, our ways for God’s, and to place our lives under His direction. “Blessed are those who do his commandments” is just another way of saying “Walk before me, and be blameless” (Rev. 22:14; Gen. 17:1). The Abrahamic covenant will be fulfilled only to those who like Abraham believe and obey.