Even if someone refuses to change, the permission of murder in the vague view of justice is wrong. Killing a serial killer doesn’t bring their victims back, killing a rapist doesn’t undo the rape they committed.
In America, our thing is “We’d rather have 8 guilty men walk free than 1 innocent jailed” (supposedly), yet there’s been more than zero people who did not commit any crimes, yet were killed. You can’t undo murder. At least if someone is given life in prison, you can set them free.
Let’s not forget that we’re more prone to give the death penalty to BIPOC inmates, not white.
And it costs more to kill someone, than to house and feed them.