Some people just don't get the cost thing!
People sentenced to life in prison are going to appeal as well. However, as the courts weigh their appeals, nothing changes. They're still in prison, however as the courts weigh appeals of a condemned man, the execution date will be postponed and postponed and postponed and postponed to the point where its just as likely a condemned man will die in prison of natural causes than see the gurney. Meaning that a death penalty can wind up costing at least as much because the individual may spend just as much time on death row as they would if they received life in prison. So in a lot of ways a death penalty is like Life + in terms of cost.
Its very difficult to actually get your case completely overturned on appeal, but far more likely to get your death sentence overturned. Increasing the likelihood that an individual sentenced to death will just wind up spending life in prison, and also why death row inmates will aggressively file more appeals than lifers. Since 1976 20% (279/1386) of individuals have had their death sentences commuted to life in prison for reasons of clemency.
Also, it isn't JUST the appeals process, but also the trial itself is very, very costly. Do you have any idea how much money Judges and Lawyers cost? Its pretty outrageous. The death penalty trials cost way, way more than trials where that is off the table.
All of these costs are necessary to help ensure innocent people aren't put to death, and even WITH these costs many people are exonerated after being sentenced to death and/or executed. The US has executed 1,386 people since 1976 and 153 people have been exonerated. (The 153 doesn't include the 279 above commuted to life for clemency reasons). Not to mention innocent people who were put to death who haven't been exonerated of which we have no idea, but I'm pretty confident we can infer that there's more likely than not a number of them as well.
Are you comfortable with murdering 1 innocent person for every 10 guilty? In a system which is already less cost-effective and contributes less to society?
Everyone says things though like 'but we KNOW that guy did it, can't we just kill him?' sure I understand, but what are we going to do? Draft a law specifically for 'that guy' and try him under a special set of rules because, come on, everyone knows he did it? It doesn't work like that, law has to be a one size fits all deal and there is no death penalty legislation that we can draft which won't wind up costing more even if you're okay with a 10% failure rate. I can only imagine how much it would cost if we wanted to ensure 0%.