God simply banned them from immortality, but this immortality involved more than physical life, but spiritual life as well. By Adam’s act of disobedience, which was a denial of God’ authority as God, a denial of His very godhood, IOW, Adam moved himself away from God, and therefore away from life itself. Adam disbelieved God.
Eating from the Tree of Life would’ve amounted to a positive step closer to God. Adam wasn’t ready for that yet. Man must learn of his need for God, to not only in order to exist but to exist in supreme and perfect happiness and wellbeing. God apparently deemed it worthwhile that man should taste of death, of the evil and sin and pain and meaningless that results from separation from Him. Adam thought he would gain from that autonomy. We’re here to learn otherwise.
In John 10:10 Jesus tells us, “The thief comes only to steal and kill and destroy; I have come that they may have life, and have it to the full.“
Jesus restores us to life by reconciling us with God, so that we may have communion with Him as is the right and just order of things for man. Jesus is that life, “the way, the truth, and the life”. John 14:16
“Apart from Me you can do nothing.” John 15:5
Turning to Him in faith now, finally, is man’s positive step closer to God, to eat from the Tree of Life.