The notion those dead and enslaved by sin want to choose Jesus is refuted by scripture from beginning to end. None want to be saved. Adam did not ask for change; he blamed God for his actions! Later, when the effects of Adam's misbehavior became prominent, God looked down on the earth and saw the wickedness of man was great, and that every intent of the thoughts of his heart was only evil continually. Everyone is/was dead in sin, and no one understands, and no one seeks God. Jesus himself looked his own disciples in the face and said, "You did not choose me, I chose you and appoint you to bear fruit." The mind of flesh is hostile to God; it does not and cannot please God. The natural man does not understand the things of the Spirit; they are foolishness to him, and he cannot understand them because they are spiritually discerned. The flesh works to bear enmity, strife, division, idolatry, rivalry, dissent. Peace and love are fruit of the Spirit.
Yes, the word of God will save all if they want to be saved but none want to be saved. God must work to that effect with the purpose to change the want of sin into a want of God as LORD.