What is the purpose of calling out individual sins if God's mercy nullifies them?

Some non-Christians make good points about the incompleteness of Christian teachings on forgiveness particularly like this one: christian forgiveness its a bug not a feature. However the focus is most often on how the benefits of forgiveness are not obtainable by the person who has been wronged.

The Catholic Catechism stipulates that forgiveness from God can only be provided to those who have "Satisfaction":

Satisfaction

1459 Many sins wrong our neighbor. One must do what is possible in order to repair the harm (e.g., return stolen goods, restore the reputation of someone slandered, pay compensation for injuries). Simple justice requires as much. But sin also injures and weakens the sinner himself, as well as his relationships with God and neighbor. Absolution takes away sin, but it does not remedy all the disorders sin has caused.62 Raised up from sin, the sinner must still recover his full spiritual health by doing something more to make amends for the sin: he must "make satisfaction for" or "expiate" his sins. This satisfaction is also called "penance."

1460 The penance the confessor imposes must take into account the penitent's personal situation and must seek his spiritual good. It must correspond as far as possible with the gravity and nature of the sins committed. It can consist of prayer, an offering, works of mercy, service of neighbor, voluntary self-denial, sacrifices, and above all the patient acceptance of the cross we must bear. Such penances help configure us to Christ, who alone expiated our sins once for all. They allow us to become co-heirs with the risen Christ, "provided we suffer with him."63

The satisfaction that we make for our sins, however, is not so much ours as though it were not done through Jesus Christ. We who can do nothing ourselves, as if just by ourselves, can do all things with the cooperation of "him who strengthens" us. Thus man has nothing of which to boast, but all our boasting is in Christ . . . in whom we make satisfaction by bringing forth "fruits that befit repentance." These fruits have their efficacy from him, by him they are offered to the Father, and through him they are accepted by the Father.64

Thus, to obtain this "Satisfaction" it would make sense the person compensated those who they have wronged. A human can not be satisfied while knowing another will not give them forgiveness for what they have done wrong.

Though the word "Satisfaction" hardly does the concept any justice, it is important to note the deep reaching implications of such a concept. Say a minister gives someone the penance of eating cake, for all the bad things they did. No one could feel satisfied upon such a penance, thus they are obligated to attend confession with another minister until they are satisfied. Hopefully this gives people a glimpse into the importance and numerous implications of "Satisfaction" in the process of forgiveness.

However, this kind of propping up "forgiveness" makes many Christians forget the reason for such a concept in the first place, to refocus efforts on making a better future by correct actions in the present. This is how the best compensation can be made, by those who have done wrong conducting good actions in everyday life. The death of the evildoer only provides compensation to those with hard harts.

I think you are forgetting the next line (1 Corinthians 6:11):

And this is what some of you used to be. But you were washed, you were sanctified, you were justified in the name of the Lord Jesus Christ and in the Spirit of our God.

It seems to me that Paul is listing those sins as examples of evils that one may do to another; however, the emphasis does not seem to be the sins specifically; rather, Paul shifts his attention toward his conclusion: being sanctified by having faith in Jesus.