Covenants identity and details

One of the arguments that modern evangelicals post against covenant theology is that of identity.  They say,  "God called the Israelites his people. He would not leave them just in order to embrace a different bunch of sinners."
But then it occurred to me. God didn't leave the Israelites, they left him.  There is a  regular pattern in covenant theology.  Each time the current leader of the covenant dies, the rest of the people fall into horrible sin.  Judgment them upon falls, God raises up a new leader,  leads  some of the people through that judgment, and gives more details of his covenant.
This is exactly what has happened with Jesus Christ.  Jesus took the identity of Israel upon himself,  suffered the judgment for Israel's horrible sin,  but God raised him up and lead the few faithful Israelites through that judgment.
He has now given them/us the New Covenant.  God didn't turn his back on the Jews.  He provided a way for them to pass through the judgment against the Old Covenant unfaithful.  Those that listened and followed the new covenant head came into new life and the New Covenant.  Those that didn't turned away from his offer of salvation.