Thank you for making this post. It provides an opportunity to consider this error which I have heard others make yet not articulate, so while I see some serious problems with this view, I am glad we can now discuss this topic.
This view denies some of the essential attributes of God such as His unchangeable nature. The God of the Bible is not a capricious or changeable God as is man. When we attribute such characteristics to God, we essentially create and idol, a god of our own making. A god made after our own image. This is not the God of the Bible. He is the same, yesterday, today and tomorrow, He is unchangeable.
Regarding the wrath of God towards sinners, I would like to commend to your reading the article "The Wrath of God in Relation to the Atonement" by Frederick S. Leahy The doctrine of God is essential to our understanding of scripture that I think you might gain much from reading this for, "If we are wrong in our doctrine of God, we are wrong all along the line. We shall be in error in every doctrine of the Faith if we hold an erroneous doctrine of God. So our doctrine of God will relate powerfully to our doctrine of the Atonement. If, for example, we do not believe that God is a God of wrath as well as a God of love, and that his essential holiness means the inevitable punishment of sin, then we shall not believe in the substitutionary and vicarious nature of Christ’s death on the Cross. That is why the doctrine of God’s holy wrath borne by his Son at Calvary is repugnant to the liberal theologian. He has an erroneous view of God."
If you will read this very short piece, I think it might clarify some essential issues for you. The Wrath of God in Relation to the Atonement