The central problem of the Penal Theory is, as you point out, understanding how punishing a person other than the perpetrator of the wrong can meet the demands of justice. Indeed, we might even say that it would be wrong to punish some innocent person for the crimes I commit!
It seems to me, however, that in other aspects of human life we do recognize this practice. I remember once sharing the Gospel with a businessman. When I explained that Christ had died to pay the penalty for our sins, he responded, “Oh, yes, that’s imputation.” I was stunned, as I never expected this theological concept to be familiar to this non-Christian businessman. When I asked him how he came to be familiar with this idea, he replied, “Oh, we use imputation all the time in the insurance business.” He explained to me that certain sorts of insurance policy are written so that, for example, if someone else drives my car and gets in an accident, the responsibility is imputed to me rather than to the driver. Even though the driver behaved recklessly, I am the one held liable; it is just as if I had done it.
Now this is parallel to substitutionary atonement. Normally I would be liable for the misdeeds I have done. But through my faith in Christ, I am, as it were, covered by his divine insurance policy, whereby he assumes the liability for my actions. My sin is imputed to him, and he pays its penalty. The demands of justice are fulfilled, just as they are in mundane affairs in which someone pays the penalty for something imputed to him. This is as literal a transaction as those that transpire regularly in the insurance industry.