There's a difference between 'fails at the extremes' and 'never worked a little'.

In a society where life is cheap and legal advancement is painful and opportunities are rare, you'll have the situation you mention. If the law is always fatal but rarely applied, why consider it at all?

In a comfortable society that has free food for everyone, a wider range of punishments actually does tend to control crime. In my country Murder can get you (effective) life, and selling marijuana on the street can't. You can buy joints easily but hitmen remain scarce.

The fact that crime still exists doesn't mean that public, extreme, and/or gruesome punishment doesn't act like a deterrent which reduces the frequency of crime. I'm not saying that inhumane punishments it necessarily justified, but this argument is fallacious.

The crime was 20x worse and more common back when we had death penalty.

Comvined with the fact that most EU countries have much lower crime rate than US and have no death penalty, it shoupd be clear that death penalty is totally ineffective at reducing crime. There is literally no place on earth where you can demonstrate "we introduced death penalty and crime has fallen" by any significant amount. We do, however, have ironclad proof that rehabilitation makes a difference. We have proof that quality of investigators that make sure the perpetrator is caught for sure makes a difference.

Recently in UK our inconpetent government has reduced the amount of police resources avaliable to investigate crime. More crimes are unsolved, crime rates increase because criminals are unounished, and they are hoping to compensate with tougher sentences. And that iduotic because we know it doesnt work, it never did

>Comvined with the fact that most EU countries have much lower crime rate than US and have no death penalty

Comparing US to EU is not valid in this context because we have different demographics and culture surrounding most criminality in the US. And deterrents have different levels of effectiveness depending on the individuals and cultures onto which they are introduced.

> And that iduotic because we know it doesnt work, it never did

I would question statistics on the subject given that, presuming "tougher" means more likely and longer imprisonment, literally reduces crime by removing criminals from society. There is an enormous confounding factor in that policing has been reduced, so it's going to be very difficult to tease out how much more (or less) crime would have increased without stiffer penalties.

Again this is not a value judgement, just pointing out that the fact that crime exists does not mean that deterrents don't work. That said, I presume the kind of person willing to commit a crime with punishment in range of the death penalty is probably not likely to be the kind of person who responds to deterrent - but I wonder how likely such a person can possibly be "rehabilitated".

But the argument that it does deter is also weakened. It's unfalsifiable if the response to "we removed the death penalty and crime did not increase" is "maybe crime would have started falling, and removing the death penalty prevented that". (I know that's not what you said, but it's an extension of the argument you describe.)