Babettes Feast, the largest number of innnocent people dying is the number of victims of killers, not the number of wrongly convicted.
1. Recidivism: I do not want to pay US$100,000+/year to keep alive killers who torture their victims or kill them in horrifyingly cruel ways. These killers usually fit the profile you outline for recidivists. I see no point in paying for them to moulder in prison, infecting the minds of people who will be released.
2. The money: Again, I say that money could be better spent and often is. Governments do this all the time. It's called the budget process. Each year when the state legislature passes a budget there are discussions about how to spend collected revenues. I've sat (as a visitor) in the state legislature of a death penalty state when lawmakers were deciding whether to spend more money on prisons and incarceration or on programs for mainstreaming handicapped people, or on mental health facilities, or on public housing for poor people. This happens 52 times every year in the United States. That's once per state, the District of Columbia and the federal government. Did you know the United States is the number provider of foreign aide? The amount has gone down in recent years, at the same time that money to run prisons has gone up. IT HAPPENS ALL THE TIME.
BTW, in the US it is illegal for prisoners to do work that would compete with private industries so it is not possible for them to earn their keep.
3. War IS relevant to this topic. It is "state sponsored killing," which is one of the objections to the death penalty. And yet some people who are against the death penalty on these grounds are for "peace keeping" actions that involve the deaths of many innocents in the interests of protecting many more innocents. That is the point of the death penalty. Same thing.