I absolutely guarantee that people who are pro death penalty don't actually think about it

Well, your absolute guarantee is wrong. I have thought about quite a lot, and come down on the side of being pro-death penalty.

The very rare “wrong” (and yes, it is inevitable) is balanced by the societal satisfaction/retribution/justice of getting rid of Ted Bundy and similar, terrorists like Timothy McVeigh and similar, and family annihilators like John List and other egregious murderers rather than have them hang around painting pictures and enjoying another 40 years of life on the taxpayers dime.

As for “who will do it”, well, I’d offer first opportunity to the victim families, but if they decline I’m sure there would be a long line of volunteers for the task.

It doesn’t even occur to them that the justice system is far from perfect anhd innocent people can get caught up in it

Sure it does. Stop pretending you know what the pro-penalty crowd thinks. You’re setting up strawmen and then heroically knocking them down. You’re simply wrong, “absolute guarantee” or not.