Yup, always a misunderstanding of Paul's Epistles alone.
But let's refute the misinterpretation from Paul himself.
So why does wrath come? Because God just arbitrarily damns some?
Not at all. It is clearly explained by Paul in multiple places.
Ephesians 5:6
5For of this you can be sure: No immoral, impure, or greedy person (that is, an idolater), has any inheritance in the kingdom of Christ and of God. 6Let no one deceive you with empty words, for because of such things the wrath of God is coming on the sons of disobedience.
Hence, the Wrath of God comes only because of immorality, impurity, greed etc. Not because God arbitrarily condemned anyone without their own fault.
Colossians 3:6
5Put to death, therefore, the components of your earthly nature: sexual immorality, impurity, lust, evil desires, and greed, which is idolatry. 6Because of these, the wrath of God is coming on the sons of disobedience.
Again, the Wrath of God comes upon the sons of disobedience which means, in theological terms, the reprobation of God is consequent to their disobedience.
I guess Calvinists will understand those terms: in simple language, it means no one goes to hell unless he does one of these damnable or deadly sins in willful disobedience which God has commanded us to avoid.