This should be a un-ignorable reminder of the value of due process. Better a guilty person go free than an innocent person sent to their long, slow, undignified death.
This is a scale thing though right? You'll have some false convictions if you want a justice system. Nothing is perfect, breakage inevitable.
Nobody wants to be the victim of a miscarriage of justice themselves, but everyone wants crime to be dealt with effectively. The trade offs are real and I suspect the average person has an acceptable non-zero rate in the back of their mind
Perhaps this is an assumption you are making which is not true.