Secondly, and I'm sorry, but your characterization is incredibly sloppy. The overall outcome is better if even one exoneration happens and you assume equal preference for life imprisonment vs execution. However:
* Many wrongful convictions will be exonerated. There are multiple per year. There has been at least one this year: https://deathpenaltyinfo.org/innocence-cases#CliffordWilliam...
* Further, while the preference might not be "infinite" you can just look at the overwhelming majority - innocent or not - of death row prisoners that exhaust all avenues of appeal to see that there is a strong preference there.
Secondly, of course I don’t dispute that there’s generally a preference for life imprisonment over execution.
From the perspective of the - potentially falsely - accused, "The difference is that you’re still alive" is a pretty fundamental distinction and "The finality of imprisonment and execution are the same" is false.