Atonement by crucifixion

Historically, many Arminians reject penal substitution. They agree with Calvinists that if Jesus died to satisfy God's justice on behalf of the redeemed, then all the redeemed must be saved, since there's no judicial basis for them to suffer eschatological punishment. In addition, progressive theologians like Randal Rauser find the idea of penal substitution repugnant.

Proponents of penal substitution quote and exegete the standard prooftexts. And I think those carry the day.

There is, though, a neglected, but straightforward argument for penal substitution that doesn't rely on the standard prooftexts. Hidden in plain sight is Christ's voluntary death by crucifixion. 

It can't be seriously doubted that the Gospels (indeed, the NT generally) present the Crucifixion in vicarious, sacrificial terms. If, however, Jesus didn't die a penal substitutionary death, then why did he choose death by crucifixion? Why did he undergo a type of death that's emblematic of vicarious sacrifice? If penal substitution is false, why did he die a violent death at all? If penal substitution is false, why did he have to undergo any kind of death? Whatever the alternative to penal substitution, it doesn't require death, does it? Much less a death with vicarious, sacrificial connotations.

Perhaps opponents of penal substitution will attempt to drive a wedge between vicarious atonement and penal substitution. If so, in what respect is his voluntary vicarious death not punitive in character?

A last-ditch argument might be to claim that Jesus never intended to die by crucifixion; rather, he was overtaken by events. His death, or mode of death, was due to unforeseeable circumstances.

But in the Gospels, Jesus deliberately and repeatedly provokes the authorities, knowing full well that he is courting execution. Moreover, he eludes the lynch mobs. He eludes death by stoning. So Jesus is very single-minded about how he will die. 

Likewise, at his trial, he makes statements that are incriminating from the viewpoint of his accusers and judges. And he refuses to defend himself before Pilate. So, by process of elimination, he leaves the authorities with no other recourse. He systematically engineers his death by crucifixion.  

But if penal substitution is false, he was sending a very confusing message to onlookers. How else could the disciples be expected to interpret his death?