The expensive part is largely the (comparatively) exhaustive appeals process, which means counterintuitively the innocent may be even worse off now that they won't be on death row.
Here you probably mean the innocent wrongfully convicted, but I wonder how an exhaustive appeals process affects the innocent living victims and innocent family members of victims of a rightfully convicted criminal. That they’re forced to relive the trauma of passed crimes again and again every time the death sentence is appealed for over a decade in most cases. It cannot be good for them.
Much better for all involved to reopen a case if and when new evidence of wrongful convictions become convincing enough.