That is the theory proposed by more recent lawyer theologians, but not among the theories of the church in at least the first five centuries. Penal substitutionary atonement (PSA) is not something the Bible teaches. It is something you have been programmed to see in scripture by advocates of the system. The proof of this is that you cannot see the logic of a different understanding of the very same scriptures you use to defend PSA. Are you able to see the reasonable logic in my exposition of those verses from Is 53 ?If a person does not allow the innocent "Lamb of God" to take over his (or hers) burden of sin then said person cannot survive into the new world.
The whole point (throughout the OT and NT) was for a substitute to be given to bear the penalty of sin. One who was innocent and without sin (flawless/without blemish), dying so the guilty may live.
But, of course, the guilty must be willing to accept Jesus on the cross in order to become sinless and innocent again.
It's like carrying a heavy bag over your shoulder. It bows you down, makes you stumble, will eventually kill you. Someone comes along and takes away that burden from you. But you must be willing to let it go. Let Him take it away.