I’ve said this before, but theology is an issue of finding your balance. This can happen in various ways, but one of the simplest is to pick out one element of biblical truth and elevate it above all others, ignoring, or sidelining important balancing themes. For instance, some have issues with accounts of salvation that emphasize, or indeed, merely teach that God does not accomplish his forgiveness apart from atonement. Is he not a loving Father? Do not fathers forgive all the time without requiring payment or retribution? If even human fathers can do so, how can our heavenly Father be any less merciful or gracious by requiring satisfaction for sins?
Bavinck shows us the problem with that sort of thing:
God is most certainly the Father of humankind, but this name is far from describing the entire relationship in which God stands to his creatures. He is also Creator, Maintainer, Ruler, Sovereign, Lawgiver, Judge, and so on, and it is one-sided and conducive to error if one takes one of these names—disregarding all the others—to be the full revelation of God. Thus, in relation to sin, God is not just a creator or injured party who can cancel the debt and forgive as well as forget the insult but is himself the giver, protector, and avenger of the law, righteousness in person, and as such he cannot forgive sin without atonement (Heb. 9:22). In that capacity he cannot nullify the just demands of the law, for we are not speaking here about personal or private rights, which one can relinquish, but about the righteousness, that is, the perfections and honor of God himself. Against this idea one could appeal to the prerogative of pardon that an earthly government frequently exercises, but this prerogative of pardon is only given to it because it is fallible and in many cases inflicts a penalty that is too severe or even undeserved. In God something like that cannot happen. He is righteousness in person, does not need to restore justice or nullify it by grace, but lets both justice and grace come to expression in the cross of Christ.
-Herman Bavinck, Reformed Dogmatics Volume 3: Sin and Salvation in Christ, pp. 372-373
Of course, one can tip the balance in the other direction and only fixate on God’s role as judge or king and forget that he is the Father who is passionately concerned to forgive. God is not begrudging in securing atonement, but gloriously willing to save sinners even as they reject him (Romans 5:6-8). Still, whichever way it happens, both make the mistake of flattening God’s relationship with his creatures by failing to account for each part of the crucial biblical imagery by which he reveals himself to us.
In other words, God gave us more than one beautiful name for himself in the Scriptures. We need to make sure we understand and worship him in light of all of them.
Soli Deo Gloria
For more on the way God’s atonement is not a denial of forgiveness, but rather the method of God’s forgiveness, see my article here.
Reformedish 
We need to be careful here. “Father” is a name of God in a way that none of the other names he lists are. Baptisms into the name of the creator, sustainor and redeemer are not valid. And we are not commanded to pray “Our Ruler who art in heaven…”
Also, the only name that is a full revelation of the Father is Jesus (not “Jesus”). And this is where, at least for me, I run into troubles with PS. To describe we need to look *from* the only name of the Father, Jesus Himself, and look instead to what we take to God’s actions toward Jesus–that is, we need to get behind the name and see instead the unnamed, and unknowable, God’s treatment of His Name. Indeed, on the Cross, we *do* see God simply forgiving sins “Father forgive them…”
We might still be able to get PS, namely, through the revelation of the pre-incarnate Logos, but even then, much more complicatedly than via our usual tack.
(Though, one also runs up into a problem that though it is true that God cannot nullify the just demands of the Law, namely, righteousness, God Himself is entirely unmoved by anything outside Himself, and so though He can take up being moved by men (at least, in a sense being moved by men), since men are divine acts, He is *entirely* unmoved by sin, since sin is in no way a Divine act, but is, rather, the absence of a Divine act.)
Though, I don’t know the Reformed doctrine well enough to know whether the Reformed make that error, and am not accusing the proper Reformed doctrine of making it.