On Jacob’s deathbed, he declares that Judah is the tribe from which a king will come. Similarly, Balaam prophesies that a king would come out of Jacob. Jer 31:31 prophesies a new covenant, and Isaiah prophesies a suffering servant whose life points to Christ. There are several covenants, those of creation, conscience, Noah, Abraham, the law, David, and the new covenant of Christ, each building on the other.
God has been willing to come to man and be intimately with us, as the word immanuel, God with us, implies, but the priesthood is instituted to keep us from transgressing, by holding us to the service of God, and acting as a buffer between man and the holy things.