Just like someone who believes that you freely choose to believe in Christ gets accused of "self salvation" or salvation by works and just like Calvinists are accused of slandering God and having a view of a monster of a God - you have the same things happening with penal substitution.
As you said it, if the idea is that God, because of being offended by our sin, is full of wrath and is just wanting to punish someone, big time and fortunately for us, Jesus steps in and says "If you have to punish someone punish me", and then he takes it for us to placate the vengeful God, then I don't believe it either.
But if God the Father, and the Son, being separate and yet also one, in counsel with each other in perfect love and harmony and with the wisdom they have that is totally above all of us, after determining that for the sake of justice, our sin by way of being part of Adam and by our own actions must be punished. If they came to decide that the method of the cross, with Jesus shedding his blood and dying, was the right way for God to judge sin, as well as satisfy His wrath, which he poured out on His Son, who was uniquely qualified to act as a suitable substitute for us by virtue of being one with the Father as well as a true human and sinless so that he could represent us and facilitate our redemption and reconciliation with God. I can believe that and dare not be repulsed by it.
I get very uncomfortable when people start questioning God's motives and how much justice or punishment he required and so on. When we get into that area I think we are on the verge of blasphemy. We know about the crucifixion and we know that Jesus felt impelled to go there so it must have been important to us and to the Father who in His wisdom did not take the cup from Jesus when he prayed. We have multiple scriptures showing this from Leviticus to Hebrews.
I admit some express PSA in awkward ways that aren't helpful but while I suppose you can reject certain expressions or tones of explanation as being not helpful I don't see how, if you reject the idea that God was dealing with our sin with Christ on the cross, directly, by his blood being shed and his death - in that case I don't think you have the gospel right.