Dr. James Anderson explains how the denial of the atonement is an issue for Islam:

The obvious problem with this response is that it openly equivocates on the term justice. In essence, it argues that God sometimes “concedes justice” (“in its first sense”) in order to satisfy justice in some other sense (“justice is at work in a different way”). But it’s hard to see how this actually solves the dilemma I posed in the book. Justice by definition entails exacting the due penalty for a sin or transgression. If a sin goes unpunished, justice has not been done. The Quran itself underscores the justness of Allah’s judgment with its vivid imagery of the scales:

We shall set up scales of justice for the Day of Judgment, so that not a soul will be dealt with unjustly in the least, and if there be (no more than) the weight of a mustard seed, We will bring it (to account): and enough are We to take account. (Q21:47, Yusuf Ali translation)

And We place the scales of justice for the Day of Resurrection, so no soul will be treated unjustly at all. And if there is [even] the weight of a mustard seed, We will bring it forth. And sufficient are We as accountant. (Q21:47, Sahih International translation)

If Allah forgives a sin by merely deciding not to punish it (“concedes justice and acts mercifully”) then whatever else it might be, it is a failure to exact justice. Suppose that two people are convicted of exactly the same crime, but the ruling authority decrees that only one of them will be punished. Wouldn’t that be unjust?

The problem with the Islamic view of Allah’s forgiveness, as a mere suspension or nullification of the demands of justice, is brought into clear view by this well-known hadith:

The Prophet said, “Amongst the men of Bani Israel there was a man who had murdered ninety-nine persons. Then he set out asking (whether his repentance could be accepted or not). He came upon a monk and asked him if his repentance could be accepted. The monk replied in the negative and so the man killed him. He kept on asking till a man advised to go to such and such village. (So he left for it) but death overtook him on the way. While dying, he turned his chest towards that village (where he had hoped his repentance would be accepted), and so the angels of mercy and the angels of punishment quarrelled amongst themselves regarding him. Allah ordered the village (towards which he was going) to come closer to him, and ordered the village (whence he had come), to go far away, and then He ordered the angels to measure the distances between his body and the two villages. So he was found to be one span closer to the village (he was going to). So he was forgiven.” (Sahih al-Bukhari, 3470; cf. Sahih Muslim, 2766b)

This man murdered a hundred people (and how cold-blooded that last murder was!) but because he repented he was completely forgiven; he received no punishment at all. But that’s not how justice works. Repentance can’t be a substitute for a just punishment. Claiming that this satisfies some “different way” of justice, some “higher principle” of justice, is to arbitrarily redefine the notion of justice. One has to suppose that on the Day of Judgment those hundred murders were simply missing from the “scales of justice.”

So I don’t think this is an adequate response to the problem at all. It is an ad hoc solution, claiming that Allah sets aside justice for the sake of some higher principle, but it doesn’t give us any explanation of how that doesn’t still amount to an injustice. As I noted in WYW (and this is not a novel observation) Christianity has a solution to the problem (Romans 3:21-26) that is unavailable to Islam. You can dispute that solution if you wish, but at least it makes a serious attempt to explain how God can be merciful without abandoning his justice.

A Muslim Defends His Worldview – Analogical Thoughts (proginosko.com)