Because you don't sound like you actually want justice. You sound like an angry villager from medieval times.
Death penalty is such an archaic way of thinking and doesn't serve any purpose other than satisfying our personal bloodlust. Justice means doing the right thing even at great personal cost, which as Gypsiyee pointed out is actually monetarily more efficient. Truthfully I always assumed that keeping someone incarcerated cost more than executing them (which I think most assume), but that never mattered to me. I could never justify giving any group of people the power of life and death in which that choice is based on an imperfect system. Even under the assumption that it cost more to incarcerate someone for life, I felt that it was society's burden to do the right thing and mete out justice while still leaving room for correcting mistakes.
As for culling the gene pool, I mean, really dude? By your logic we should execute the killer's parents after we get the killer. Just in case they are still poppin out murder babies. While we're at it, get the siblings too and possibly aunts and uncles. Also, in case you didn't understand this, when they're convicted for murder, chances are they won't be reproducing in jail. As for repeating the crime, it's unlikely. It's certainly possible, but unlikely and far more uncommon than an episode of Oz would suggest.
As for the pay per view TV thing, sure, I get that you're joking or maybe you aren't. I can't tell with you guys sometimes. What I do know is that anyone who is serious about that proves my point for me. They'd rather satisfy a personal bloodlust, grudge, vengeance than to actually see justice.