I want to point out that this is already the standard for conviction. The finder of fact must find the accused to be guilty beyond all reasonable doubt before convicting them. So from a legal perspective, everyone convicted of a crime already has been proven guilty to the highest possible standard. If there is any shred of doubt at all about the guilt of the accused, they’re supposed to be acquitted. It’s only possible in retrospect when new evidence emerges that exonerates the accused that it can be determined that the original guilty verdict was incorrect. You can’t really “force” this evidence to emerge with any amount of policy changes. It just happens over time.

For example, witnesses lie. Maybe five years after the fact they feel bad about lying and retract their testimony. Maybe some of the investigators assigned to the case just made up some evidence to get the accused convicted in court because they just thought there was no way he could be innocent and they just needed to cook up the evidence to get them declared guilty, and they can only admit that when the statute of limitation passes. Or maybe, three years later, a convenience store manager deleting old footage happens upon a CCTV tape giving the accused an alibi. Or maybe still, the accused was actually framed and their framers only got caught ten years later doing some other crime, and it turned out that they forged the accused’s signatures on those documents and used their computer to send those e-mails without their knowledge. I could go on.

So if your proposed standard is applied, it would not actually exclude anyone from execution because everyone who’s been convicted has already been proven guilty beyond all reasonable doubt.