It's clear from your reply that you've read closely & made an effort to hear me out despite disagreeing with me, and it's appreciated. I don't have all the answers here either; I can point in what I think is the right direction, but my understanding on this is a work in progress, and I'm not any sort of genius of sociology or political theory. I don't expect to be the person who cracks the code on the human condition. But I'll try to address your comment with the same respect you've addressed mine.
The question of how many guilty people we can let go free per innocent is like the question of how many angels can dance on the head of a pin; a vital question to which there is no answer, but which must be evaluated and re-evaluated ceaselessly. I think it's important that we keep trying to perfect society. I think it's important that we come up with utopian visions and try to implement them, knowing full well that we won't reach them. We must avoid the pitfall of looking at the tools available to us, finding them unsuited to the task, and then saying, "well, these are all the tools that I have to work with" - when we find ourselves with only bad options, what we need are more tools. Every tool we have was created by that same process.
Coercing people to follow the law with violence is just not a great plan for many reasons. There are unjust laws. There are abusive police. Fundamentally, it is a reactive system; it responds to injustices that have already happened. The idea that we punish people when they step out of line as an example to everyone else doesn't really solve the problem - if it had, surely we wouldn't be having this discussion. Desperate people will commit crimes anyway, and their punishment will only enhance their desperation. People with significant privileges realize that they can't be held accountable. Overall retributive justice treats crime as some sort of affront that demands a violent response, an eye for an eye, but I think it's more productive to think of it as a problem which demands a solution. When you view it through the lens of problem solving, it changes your perspective and what you imagine to be possible.
We should eliminate desperation and perverse incentives that lead to crime wherever possible. When that isn't possible, we should seek to detect & reverse it immediately, within the organization or community where it's happened, and excise or reprise that community member as appropriate. We should be accountable to one another, through peaceful means, and not the state through violence.
It's a common concern that, without the threat of violence, society would fall apart, as you expressed. But I don't believe that is what will happen. I think the root of this is a Hobbsian view that the fear of violence is what binds us together - if you hold this view than naturally, without violence, that binding force would be gone. But is that true of your own life? I believe people are generally motivated by care for one another more often than fear of violence. When I think about the actions I take in a given day, and I ask myself why I did them, virtually all of them are because I want to take care of the people around me. That's why I did the dishes and cooked meals for my household today; that's why I checked up on my friend who was supposed to call me, but didn't (they're fine); that's why I've been shopping for gifts; etc. I think violence in our society serves to shape our behaviors to fit a particular mold, that benefits those in power and which we wouldn't submit to voluntarily. But without that violence, I think we would still have a society, and a more just one at that. It hijacks our society for a particular purpose, but it isn't the glue that holds it together.
It's easy to find ways my ideas are imperfect, I'll readily admit that. You can't simply detect and reverse murder, being an obvious one. I'm not so naive as to think a perfect society can be achieved without perfect humans, and I don't see that as a real possibility. But I hope I can convince you that it's worth looking at things from a problem solving perspective, rather than a coercive one.