I think the ultimate punishment makes up for the lost time.
About as much as a death sentence. Thing is, you have to correct it before the final hour. Plenty of innocents have rotted in jail and died/were murdered. What's the difference? I could see your point if the US was recklessly executing people, with no appeals, and a bullet to the back of the head within days, but they're not. They put the same due diligence into making sure they got it right, the same as they do LWOP perps.
Oh' boo hoo. The law isn't run on feelings of the families of pieces of shit. ALL that shit is on the perp. If they didn't want to cause their own family pain from their execution, they should've made better decisions in life.