The free choice which Adam and Eve had was between believe God or believe Satan. They had no knowledge of good and evil.
We, we aren't born in Adam's upright state. We are born fallen creatures, and can not choose betwixt good and evil...whilst in that fallen state. That's why one must be born from above, regenerated, quickened, made alive, etc. Once God has regenerated us, we can then chose to do that which is good. In a fallen state? Not so much...
The issue is not choosing between good and evil, never has been. Adam had no knowledge of good and evil, but he was given the freedom to choose between believe God or don't believe God. This freedom of choice has never ceased. This is why God pleads all throughout Scripture for all to believe. Calvinist blind themselves to all of these pleas in favor of a flawed theology.
For whatever reason, God thrusted him out before he could lay hold on the Tree of Life. That much we know. Did Adam have a desire to go to that Tree after he fell? I don't know, but would lean towards no. Why? Read Luke 16 and the Lazarus and rich man story. Even in the flames, as he communed with Abraham, not once did he ask Abraham to get him out of the torments of these flames. The Spirit was not drawing him, God was not working a will and a do according to His good pleasure whilst he was in those torments. So, Adam, IMO, had zero desire to go to that Tree of Life
For whatever reason?? We are specifically told why. Question is, why do you choose to whisk it under the rug? God certainly understood Adam could freely take of the tree of life and says so, thus He has to block Adam from doing so.