Forget about deterrence, or the punishment fitting the crime. What matters is that punishment applied is relatively more severe for crimes that are worse than others. For any level of punishment, think about for what crimes that punishment is meted out. Then think of another type of crime. Is it worse or not as bad as the first crime? If worse, the punishment should be greater. If not as bad, the punishment should be less.
Now think of crimes that rate life in prison. Is murder worse than those crimes? If it is, then the punishment should be more severe. What punishment is beyond life in prison, if not capital punishment? Technically, torture would be worse, but we can't do that.
The troubling thing is how horrible the jury system is. We have jurors who vote guilty when the "evidence" only suggests a defendant is guilty. To counter this, these jurors should be held responsible for their actions. If a person is later found to be innocent, the jurors should be forced to pay monetary compensation to the person whose life they ruined. Perhaps then jurors would start to actually use the "reasonable doubt" threshold.
Unfortunately, with the broken jury system, we can't use the death penalty the way we should. We know that juries convict innocent people so we have to have long periods of review to resolve the problems that they cause. We must not allow innocent people to be executed. Better 99 guilty people go free than one innocent person be found guilty.