Prison can be stopped any time and the person declared not-guilty can be compensated for any prosecutor/police misconduct.
Death is absolutely final and several people have been declared not-guilty after the fact.
You’re never going to have absolute certainty.
Videos can be doctored. Confessions can be coerced. Witnesses can be bribed.
You can explain to a father whose daughter was raped until she dies as to why the inmate, whose conviction is almost certain why he gets to live and others do not.
You are also the sort of person, where because real justice is almost unattainable, that many people cheer inhumane prison conditions or prison rape because they no longer have faith in a justice system that will give them justice.
In all trials, every means should be used to best determine guilt or non-guilt, but once an accused is found guilty, thre should be little hesitation in carrying out the sentence.