Several reasons.
The animal was not sacrificed instead of the people. Had the animal not been sacrificed the people would not have taken its place.
If I may interject some thoughts…
A sacrifice cannot ever be the individual who needs the sacrifice. If I am punished for my sin, I am not sacrificed for my sins, I am judged for them with no atonement available. There is no sacrifice.
So as I read what you say, I think you have taken the instead of too far.
Also, animal sacrifices are teaching tools and not able to take away sin. So there is not even the remotest possibility that you would sacrifice a person instead of an animal. An example is the redeeming of the firstborn. An animal could substitute for another animal or be taken for sacrifice itself. But in redeeming the firstborn child failing to redeem them was not an option. Redeeming the firstborn is a clear example of the instead of principle.
When you eat a hamburger the cow was not slaughtered instead of you (although if you do not eat you will die).
This is not a bad example. One life given to sustain another.
Jesus gave the same example with water with the woman at the well. He also declared Himself bread to be taken in. (Not transubstantiation)
What would have happened if the animal was sacrificed but the priest did not "make atonement for the sins of the people" by applying the blood in the Most Holy Place? The people's sins would not be atoned.
But that never actually atoned for sin or it would have ceased. So the example is imperfect whereas Christ is the perfect sacrifice.
No, sacrificing an animal is not penal. Here yoy drift from Scripture and the Hebrew practice. The atoning sacrifice was viewed as a "gift" of obedience (think of Jesus' obedience even to dearh on a cross).
They were not punishing these animals. The animals were not facing a penalty. They were being sacrificed (actually in a humane way - the animals were not experiencing suffering).
If you showed up without an offering the priest would not grab you and slit your throat and offer you as a human sacrifice to God.
You cannot say that Jesus did not suffer. It was not a vacation from heaven that Jesus was taking. Jesus was tried in court. Jesus was condemned to die. That is penal. It may have been a corrupt court but it was the sentence of a criminal that Jesus received.
When the people sacrificed an animal they were not punishing the animal. The animal was not being killed instead of the people.
Just a picture and not the real thing.
Our chastisement, our punishment was on Jesus.
The animals that died in medical research to develop cancer treatments did not die instead of those who receive the treatment. They died for the purpose of developing a treatment but not "instead of"".
You have singled out an example instead of Christ the real sacrifice. So the example, the schoolmaster to point us to Christ you may find fault in. But you have not shown that Jesus did not die for our sin instead of us. You have only shown that animal sacrifices are not atonement instead of us.
But Jesus tasted death for us. It removes death from us. So I don’t see any problem yet with instead of.
Isaac was taken to be sacrificed but the sacrifice God provided was sacrificed literally instead of Isaac. Isaac was removed and the ram sacrificed instead of Isaac.