Here in Ohio, they recently put to death a person who had killed a convenience store clerk and had knocked over a couple other stores that night.
In 1983. This guy was on Death Row for almost twenty years, with appeal after appeal after appeal after appeal. And after seventeen years of that, the defense "discovered" new evidence and they went through a couple more rounds of appeals, with various stays and rulings by judges.
That's not cost-effective at all. You'd spend far less to lock him up for the rest of his life than to keep going through this sort of appeals process. Certainly you don't go through anything like this for life sentences..