As it turns out, they're not particularly effective. The people who go and hold up a convenience store aren't doing it because of a reasoned cost-benefit analysis based on risk of capture, differential value of prison vs freedom, and future discount rates. They're doing it because they don't do those things.
That leaves three real reasons:
2) Reducing society's exposure to criminal elements
3) Punishment as a moral good in itself, as a way to rectify injustice.
Conversely, at least some percentage of the people who don't have made that cost-benefit analysis.
Plus some part of the people who go and commit felonies, mainly the young and naive, have made at least some basic cost-benefit analysis; they mistakenly think they'll be the leaders/tough ones in prison and it'll be okay.
I'm not a fan of the punitive prison model, but fear of consequences is a good deterrent.
(I sound like an uptight prick, but I'm speaking from experience. Then again, I've never been in a US prison, so I can't say much about them and I don't like what little I know)
..In the US.
Everything you say after that needs to be filtered through the same lens. You seem to be making a global statement about why people commit crimes without a lot of support for it.
At least some proportion of the population are deterred by the possibility of being caught and punished.
I said nothing about adding ten years to sentence lengths. I don’t know, and don’t claim to know what the optimal length of sentence (or other punishment) is, except that it is not zero.
This seems weird to you because it's not how your mind works, but it's what the data indicates.
It's only a "complete" solution if you actually have the right person.
The term recidivism means "the tendency of a convicted criminal to reoffend."
Thus it only applies to the already convicted. If they weren't caught and convicted, and they reoffend, it's not recidivism.