All human systems operate on a “good enough” basis. You can tweak the knobs to trade off false positives versus false negatives in whatever balance is politically viable. But there will always be false positives, and in such a huge country even a systematically low false positive rate will generate many outrage-inducing stories of injustice.
Both election results and criminal verdicts are, and should be seen as, statistical determinations with error bars. All we can control is the size of the error bars, and we can control those only by trading off other things we care about (cost of the system, speed of the system, etc.)
Just focusing on error rates leaves out the details by which false positives are created, which are very important to everyone's individual sense of justice.
For example, one of your examples was "forced to plead guilty". The word "forced" implies something else responsible for the erroneous outcome. Rather than merely saying that was a "false positive" that could be tuned, we should focus on that specific thing responsible - if it was the system's high-stakes dynamics depriving a person of their right to a trial, then those dynamics need to be reformed. If it was a bad faith prosecutor/cops pushing falsities to get a baseless conviction, then they need to be criminally prosecuted for abusing the power of the state to suit their own personal ends.
Everybody knows that bad things do occasionally happen. The outrage isn't merely due to the initial miscarriage of justice, rather it's the nonchalance of the entrenched system shrugging it off rather than reifying and prosecuting its own crimes.
Both election results and criminal verdicts are, and should be seen as, statistical determinations with error bars. All we can control is the size of the error bars, and we can control those only by trading off other things we care about (cost of the system, speed of the system, etc.)