You keep focusing on your fallacious opinion that we have reason to believe that enforcing the death penalty strictly would have a positive effect, but we couldn't know that until we tried it. So, by that logic you seem to be suggesting that it's ok to risk enforcing immoral activities in order to figure out whether they're beneficial or not. Would you force people to swallow liquid drano to find out whether it's fatally poisonous and try to justify it by saying that once we know for sure we'll be better informed?
By that analogy, the death penalty absolutely is a deterrent, because that murderer is most assuredly deterred from murdering.
As far as other people are concerned, your analogy is meaningless.
A person who commits murder is far less likely to be executed than a person who drinks drano is likely to be fatally poisoned.
Therefore, more people are likely to think "bad things will happen to me if I drink drano".
Less people are likely to think "If I stab my mother in law 37 times in the head and neck, I'll be put to death"
Why?
Because people who drink drano are surely going to suffer severely, if they don't die.
People who commit murder have a better chance at getting away with it than being put to death for it.