The punishment is a sentence of death. Not "being killed". You are to be placed in the state of death for the crime. That's why you don't get to walk away if a lethal method fails. You can keep reviving them, but they'll be incarcerated and killed again until it sticks. And I'll put the rest of the party in contempt of court for attempting to subjorn lawful punishment.
There's some stuff about devils and how souls are recruited for the whole endless demon war thing that implies that everyone gets re-incarnated but its usually random, while elves and devils are always re-incarnated as the same race except in special circumstances.
Not everyone. Most souls go to outer planes and just sit there. Lower planes have a special property of wiping memories through the river Styx and converting them into fiends. Which then either slowly evolve into useful fiends or much more likely are destroyed in the Blood War or eaten by night hags or higher level fiends.
I'm not really looking to get into fantasy legal dispute, but I will say that you are debating the count without even touching the core of what I said: the terms of the sentencing.
Being sentenced to death is like being sent to prison. If you step in and then juke out, you can't say "prison sentence over".
We don't specify term limits here because it's typically not a place you come back from.