Yet Adama's descendants would also have free will... right? So, sin could have appeared at any time in any of his millions of descendants.
Imagine, for example, an scenario in which Adam and Eve never sinned, Abel never sinned, but Cain did.
Then Cain would have had a mortal offspring, and Abel would have had an immortal offspring... until someone in Abel's linage sinned.
The world would be filled with mortal and immortal persons.
And now, if Cain's wife had remained obedient and pure, why would the baby inherit mortality from Cain, and not the immortality from his mother?
The scenarios can grow and grow and grow... and this is just one of many speculations that have no easy solution.
Instead, believing that Adam's body was as mortal as the body of an elephant, and that the Tree of Life is the representation of The Christ, or the Word of God, prevents all these speculations.