I didn't say a lynchmob, why do people always assume a bad implementation?

Obviously, if you intend to abduct ("imprison") or kill ("execute") somebody as punishment, then you should have very high certainty they deserve that punishment. One of the methods of achieving that is giving them a chance to defend themselves ("court process").

I don't see any difference between individuals and monopolies on violence ("states") doing this, as long as they both have sufficient levels of certainty.