In a hard case in criminal law, is there really that much of a difference between a 10-year sentence and 25 to life? Is there really that big a difference between murder and manslaughter? You can never have perfect justice, so why do we spend so much time quibbling over alternatives that would both, arguably, constitute "pretty good" justice? If someone kills someone else, we don't want to give them $64,000 and a dozen roses and we don't want to burn them at the stake. If what actually happens is in some reasonable range in the midst of these extremes, isn't that good enough?
I'm not even all that queasy about convicting innocent people. There's a very small chance that I could get convicted of a serious crime that I didn't commit in my lifetime, but there's a greater chance that I could get hit by lightning or a car or, indeed, murdered! There's a lot of bad things that can happen to you in this world, and some aren't preventable.
Which world would you rather live in: (1) a world where there was a one in ten chance you would get murdered and a one in a million chance you would be found guilty of a murder you didn't commit? Or (2) a world where there was a one in a thousand chance you would get murdered and a one in a thousand chance you would be wrongly convicted?