The capital punishment argument doesn't stand up under even a small amount of scrutiny. If you take pains to ensure that the people being killed are 100% guilty you raise the bar so much that the paltry number of people you end up killing don't save you any meaningful money anyway, on top of that you would need to plan for appeals which cost money, and there would still be the very rare case of extraordinary circumstances where you topped a 99.9% chancer who actually happened to be innocent.
If you want to save the money you need to lower the bar in terms of certainty to up the numbers, and you need to reduce the appeals process which means as a result you'll be bumping off more innocent people. If your economics and morals say that's a reasonable compromise then more power to you, I just hope you never get wrongly sentenced for murder.
The only viable argument for the death penalty is that you believe that some people or some crimes are so heinous and reprehensible that you want those people to be punished as an act of revenge in the most permanent way possible, and you're happy that some innocent people will die, or that it will cost more than it currently does, to ensure that happens.
I'm of the opinion that as a society we should be better than the murderers and rapists, and I'd rather a wrongly convicted person is incarcerated than killed. Some people disagree and that's okay, but don't hide behind economics, own the fact that you want the state to kill certain criminals as a societal revenge for their actions, it's not an invalid position.