Um, just no. Escalating punishment, and including physical punishment, is a guaranteed way to induce extreme problems. Prisons are packed with people who lived that life, listen to some interviews. Breaking people leaves broken people who break more people.
Note: I'm not saying punishments are a bad idea. But severity as the variable to tweak, that's demonstrably a dreadful plan.
Sure, just throw your certainties in my face like the truth. You name prisons, but you forget that until recently, most children were subjected to physical violence and most of them did not go to prison.
But if you read the above correctly you would understand that it is not about breaking at all. On the contrary. It is about proportionality and that is also the hard part.
We are physical beings, why should all punishment be executed on the mind? Why is torture of the mind better? Is burden someone up with a significant debt is not seen as torture, but it is. So much so that some people commit suicide.
They may not all have ended up in prison, but certainly they, on average, went on to commit a much higher level of violent crime.
Violent crimes of all types have trended downwards steeply in the time since those types of punishments stopped being accepted. We are well rid of them.
Note: I'm not saying punishments are a bad idea. But severity as the variable to tweak, that's demonstrably a dreadful plan.