The link between Penal Substitution and final judgment

I think one of the reasons that some Christians see Penal Substitution as such an important doctrine is because they link it to the final judgment. They see deniers of Penal Substitution as denying the very thing necessary for humanity to pass the final judgment. However, I think this link they make between Penal Substitution and final judgment is a faulty one. Penal Substitution need not have any link to the final judgment whatsoever. Here are a couple of example theological scenarios to illustrate.

Example 1. God decides that at the final judgment he wants to send people who had brown hair to heaven and everyone else to hell - that is his arbitrary divine decision which he makes at the beginning of time about how he's going to run the final judgment. Now it also happens to be the case that he is just and must punish sin, so out of love he sends Jesus to be a penal substitute for all humanity, and thus God's justice is dealt with. When it gets to the final judgment, God judges people based on the criteria of hair-color he had decided on earlier. In this scenario, Penal Subsitution is true, but it doesn't have anything to do with the final judgment.

Example 2. God decides that at the final judgment he is going to judge people based on their faith, that's going to form the criteria for the judgment. God doesn't feel any need to be just, and penal substitution is not true. At the final judgment he judges people based on whether or not they had faith. In this scenario the lack of Penal Substitution doesn't stop there being a judgment based on faith.

Example 3. God decides final judgment will be based on virtue, with the 10% most evil humans going to hell and the 90% most virtuous going to heaven. It also happens that he is just and feels the need to punish all sins against him infinitely. He doesn't like the thought of having to punish those 90% of people infinitely, so he sends Jesus as a penal substitute for everyone, thus removing his need to hurt them. At the final judgment he judges according to the criteria of virtue he had decided upon, sending 90% of people to heaven based on their virtue and 10% to hell based on their lack of virtue. Here Penal Substitution is true and is necessary to prevent infinite suffering for those who are virtuous, but they do not pass the final judgment based on the merits of Christ they pass it based on their own merits. Had Christ not done his thing they would be toast, but at the same time it was not Christ that caused them to meet the standard.

I have tried through these examples to explain how Penal Substitution need not have any connection whatsoever to the final judgment. I think some people make assumptions about the connection between the two doctrines and then when Penal Substitution is denied they feel particularly threatened because of the connection they have established in their mind between the two doctrines. In other words, they have made Penal Substitution artificially important in their own minds by mis-associating it with important concepts about final judgment, and thus a denial of Penal Substitution strikes them harder than it really should.