Dave, you are right. As I see it, God placed in the Garden, both the Tree of Life and the Tree of Knowledge of Good and Evil, with the intention that Adam and Eve would eat from both. But, though mature physically, they were immature mentally, emotionally and spiritually. So God’s intention was for them to first eat from the Tree of Life, and when they had matured they would be in a position to benefit from knowing the distinction between good and evil. For knowing that distinction is characteristic of mature people:
(Hebrews 5:14 ESV) But solid food is for the mature, for those who have their powers of discernment trained by constant practice to distinguish good from evil.
So God forbade them from eating from the fruit of the Tree of Knowledge of Good and Evil until they were prepared to do so through becoming mature. But Satan tempted them to do it the other way around so that they would ruin themselves. They weren’t in the mental, emotional, and spiritual condition to handle Knowledge of Good and Evil. That’s why they hid themselves from God as a result. That’s why they were ashamed of being naked.
Even though God had not commanded them from refraining from eating the fruit of the Tree of Life, they never did so. Again they did the reverse of God’s intentions, and thus He had to keep them out of the Garden, so that they wouldn’t eat from the Tree of Life and live forever in their fallen condition. For if they had lived forever as fallen people, then their wickedness would also continue to escalate perpetually.