"We have to assume the conviction is correct."

That takes quite a faith in process that has little remedial feedback.

Unlike say engineering or medicine where there can be a said to be an objectively observable system where all strive towards similar outcomes - and even those disciplines screw up constantly.

"Otherwise that leads to basically letting everyone go free just in case they're actually innocent"

There is a huge category of crime where long term incarceration absolutely does no help to anyone whatsoever.