I don't think your argument about capital punishment not deterring murder in the actions of murderers holds much weight. To gauge the efficacy of the death penalty as a deterrent, you have to measure murders against murders that were prevented provably by the death penalty. I don't think even the most staunch supporters of the death penalty would argue that it deters all murder.

Of course, it would be completely impossible to get any kind of data on how many murders people decide not to commit for the specific reason that the death penalty is in place. In my opinion, this fact alone is already a good argument against the deterrent claim. What evidence do supporters of the death penalty have that it prevents murder? I haven't seen any. Please tell me if you find some.

I agree with your conclusion, but for different reasons. This argument simply points out that not all people are deterred by the death penalty, as is evidenced by murder happening sometimes.