Back to America, the death is more expensive because....
Most defendents can't afford their own Attorney, as the trial involves capital punishment two lawyers and a prosecutor are appointed at a cost to the public.
Capital Punishment trials last generally 4 times longer than non capital, for obvious reasons. Jury Selection is long winded, most death row prisoners are kept in solitary confinement in a special facility with more security.
When the evidence is beyond all reasonable doubt then Capital Punishment should be employed, taking the accused out of the court room into a van and straight to the electric chair, firing squad, lethal injection.
Not kept on death row for years making appeals and waiting for the law to change.