Who Is to Blame for Evil?
The importance of believing in a historical fall of Adam and Eve is seen when we ask the question Who is to blame for the evil in the world today—for the sin, suffering, and death that exists? If we believe in the biblical story of the fall, then Adam and Eve are responsible. They sinned, they disobeyed God, and they brought the punishment of sin and death into the world. That's why suffering and death exist in the world, but this is not how God created us to be, so God is not to be blamed.
But if you hold to theistic evolution, then you think that the world as it is is the way it always has been. In other words, this is the best that God could do by allowing evolution to run its course. That runs dangerously close to blaming God for sin, suffering, and death in the world—something that the Bible never wants us to do.
Paul explicitly connects representation by Adam and representation by Christ.
One Man's Sin, One Man's Obedience
The other reason that it's important to believe in a historical Adam and a historical fall is that the New Testament connects Adam's sin to our salvation in Christ. Someone might argue that, if Paul was wrong about the entire human race descending from Adam as the theistic evolution advocates would say, he was perhaps also wrong about all human beings inheriting a common sin nature from Adam. If this is true, Paul could also be wrong about our gaining righteousness and forgiveness through our representation by Christ.
It's unmistakable how Paul explicitly connects representation by Adam and representation by Christ. This is what Paul says in Romans 5:17:
For if, because of one man's trespass, death reigned through that one man [Adam], much more will those who receive the abundance of grace and the free gift of righteousness reign in life through the one man Jesus Christ.
And then Paul goes on to say, "For as by the one man's disobedience the many were made sinners, so by the one man's obedience the many will be made righteous."
So, there's a clear parallel between representation by Adam and representation by Christ. If we don't have the historical fall and a historical Adam, then maybe Paul was wrong about representation by Christ as well.
In short, the entire doctrine of the atonement and our forgiveness of sins through Christ is undermined.
Explore the 12 details of Genesis 1-3 that speak to the nature of God's creation.
'Theistic evolution' actually can be a number of different distinct ideas because the term 'evolution' can have a number of distinct definitions.
Science actually got started in a very explicitly theistic—indeed Christian—milieu.