bali 9, page-33

Let's put the cost of maintaining prisoners as a plus in the case for the death penalty aside. It doesn't hold up.

If you have a death penalty you incur far more costs. It costs much much more to run the appeals through (usually) state funded defences. That takes years, even decades.

Trials where the death penalty is involved take longer and result in fewer convictions when a jury is involved because the jurors are disinclined to sentence people to death.

There are hundreds of studies on this issue. Here is one conclusion relating to California.

The authors calculated that, if the Governor commuted the sentences of those remaining on death row to life without parole, it would result in an immediate savings of $170 million per year, with a savings of $5 billion over the next 20 years.

Link

Apart from that it's barbaric, not a deterrent, and simply state sponsored murder.