If you're concerned about the "big picture," why don't you falsely confess to some unsolved murder and then waive your appeals?
Unlike mistaken convictions (which serve as a deterrent to others so long as no one meddles with them), false confessions are destructive to the system. You keep forgetting that I am the one who is SUPPORTING the system, not trying to damage it by questioning the system's results.
We're all guilty. There is only one path to Salvation.