Even if the purpose was punishment, I wonder why we harbor such a deep aversion to corporal punishment.

The (US) Constitution prohibits "cruel and unusual" punishments in sentencing, but in my mind, losing years of one's life, which one will never get back, is significantly more cruel than, say, fifty lashes.

There's a book on (roughly) this question:

https://en.wikipedia.org/wiki/Discipline_and_Punish#Summary

Cruel and unusual, not cruel or unusual.

SCOTUS has said about the death penalty specifically that it is without a doubt cruel; however, it is pervasive, and therefore not an unusual punishment. Therefore there is no Constitutional violation. I suspect a similar argument in the inverse rules out corporal punishment. Fifty lashes, even if less cruel than decades in prison, is certainly a cruel punishment. It's also very unusual for 2017 America.

Prohibitions against X and Y unfortunately tend to be grammatically ambiguous. If your read it as "prohibited to do X and prohibited to do Y" rather than "prohibited to do [X and Y]", then it is equivalent to "prohibited to do [X or Y]". So for example, the statement "It is prohibited to bring fruits and vegetables across the border" would usually be taken to prohibit bringing fruits or vegetables alone.

Ok. We can argue grammatical pedantry all we want, I'm just saying what SCOTUS has said with regard to its interpretation of 8A specifically. There are three things not allowed: 1) excessive bail required; 2) excessive fines imposed; 3) cruel and unusual punishment. The application of a cruel but common punishment doesn't fit #3.

The trouble is that punishment and rehabilitation are seen as mutually exclusive. That a "soft" prison is less punishing. But really the removal of freedom in itself is a vast punishment. Going further than that is just unceccessary and counterproductive.

The problem is rehabilitation only works on some people, and punishment works on virtually no one.

Prisons are a dumping ground for people with personality disorders. You can't fix a personality disorder with rehabilitation, or with punishment. (Arguably you can't fix a personality disorder at all.)

Some people are relatively rational. They commit crimes for a variety of reasons, a good proportion of which are a direct outcome of poverty and/or economic abuse and/or racism.

The best way to rehabilitate them is to rehabilitate society so it doesn't push them into a corner, or create subcultures where crime is a reasonable survival option.

The people with psychological issues are much harder to deal with. Keeping them locked and away and occupied is more humane than trying to "punish" them, because the punishment is pointless and will have exactly zero effect.

Running prisons as a for-profit industry instead of a social service is barbarism, and ultimately just puts more criminals on the streets.

Luckily we have a lot of data.

If punishment is rehabilitating, in average, the harder the prisons the nicer the people that come from them. We could check for instance, I don't know, Russia vs. Sweden or something like that.

If we believe prisons are to act as a sort of operant conditioning for the inmates, then the punishment IS supposed the rehabilitation. However, as you probably know, many folks do not respond to this type of conditioning.

The purpose of prisons is to keep felons away from people's children.

That's not even remotely accurate. All you need to do is look at the number of people in prison who aren't felons to know that that's wrong on its face.