Purpose of the tree of life:
Proverbs 3: 18 the tree of life is wisdom
Proverbs 11:30 the fruit of righteousness
Proverbs 13:12 hope is the desire of the heart
Proverbs 15:4 wholesome tongue
Revelation 2:7 overcomer
Revelation 22:2 twelve fruits of the Spirit and healing of the nations
Revelation 22:14 obedience
Revelation 22:19 book of life
Now, seeing all what the tree of life was for, in Genesis 3:22-24 we read that God sent Adam out of the garden so he could not eat from the tree of life.
Why, because if God did not prevent Adam from eating of the tree of life after he had sinned, a future redemption through the physical death of Jesus Christ would not have been possible.
When Adam sinned, mankind became estranged from God and physical death entered into the world by one man, Adam, death now came to all men. If Adam had eaten from the tree of life after he sinned he would have lived forever, but he would have lived in a state of eternal estrangement from God.
God knew that man would sin as God's plan of salvation before the foundation of the world was through Christ Jesus who gave His life that we can have life eternal to all who will believe in Him, John 3:16. That could not have happened if Adam ate from the tree of life and lived forever.
Glory, Rev. 22:19, says nothing about the, "tree of life," the word, scroll or book used in the texts, depending on the bible version used, is in reference to the book of Rev. itself.
Too, if as you believe, in the list of benefits from eating of the "tree of life", then why wouldn't a loving God had taken Adam and Eve by the hand and lead them to the "tree of life" and required that they eat of it, and on a regular basis, instead of barring them from it? Your understanding of it makes no sense. It is to give eternal life to those who eat of it's many fruits, from month to month, period.
The truth is, ALL of God's laws are just and righteous, and will endure forever. Adam and Eve were guilty of disobedience/sin when they ate from the tree of Good and Evil. The penalty for disobeying, any of God's laws is death by execution. Their execution that very day was, stayed only because they had no knowledge of what evil was. However, for punishment they were sent out of the garden and there conditional immortality ended, since they would not be able to eat of the tree of life, therefore, they became mortals, subject to the first death, of which there is a first or second resurrection. This is the consequences of sin, not to be confused with the penalty for sin, which is death by execution, the second death of which there is no resurrection, the wages of sin, (Rm. 6:23)
Since God's laws are eternal because they are just and righteous, they can not be set aside to save fallen man. Therefore, the Father having foreknowledge, of Adams fall, designed the plan of salvation, to save fallen man, and at the same time uphold His eternal laws.(this is what most people do not understand) This plan would require Jesus, a God Himself, our creator, to humble Himself and be born of man, to fulfill God's eternal laws by living a sinless life, that Adam and Eve and all of their descendants could not life, then die the second death, which all of mankind would have to suffer as the wages for our sins. This Jesus did, and the Father raised Him up from the second death He paid while on the cross.
Salvation is then made possible to fallen man by the grace of God through faith, by believing that God so loved the world that He gave is only begotten Son that whosoever believeth in Him should not perish but have everlasting life.
This then is why Jesus had to die, to uphold God's laws, and to pay the penalty for the breaking of the laws which fallen man could not, and still live life eternal.