You mean all of that, which still results in an estimated 4-6% of the entire US prison population being innocent?
It is not cheaper to run a proper actual system that has at least some chance of stopping miscarriages, and it will still have them so cost is not a factor.
As for deterrent, some quotes from one of last executioners in Britain, who knew a bit about it;
"I do not now believe that any one of the hundreds of executions I carried out has in any way acted as a deterrent against future murder. Capital punishment, in my view, achieved nothing except revenge."
"If death were a deterrent, I might be expected to know. It is I who have faced them last, young men and girls, working men, grandmothers. I have been amazed to see the courage with which they take that walk into the unknown. It did not deter them then, and it had not deterred them when they committed what they were convicted for. All the men and women whom I have faced at that final moment convince me that in what I have done I have not prevented a single murder. And if death does not work to deter one person, it should not be held to deter any."
I do wonder if people who say yes, would be happy to put their "money where their mouth is", and accept that all of them are put into a lottery to be chosen to be executed if any innocent person ever gets killed because they wanted the death penalty and supported it.