This is a point that feels difficult to make, but yes, to my eyes more diversity is better, even at the cost of slightly more social chaos and a rougher social landscape (with some balance).

In a way I think Japan is paying that price in that it has a harder time to adapt to change and is slower to adapt new ideas. Japanese people are inventive and come up with a lot of good ideas, but society's homogeneity and stability means the hurdle to get any idea past the critical point is that much higher. Cash is still the only payment method allowed in a ton of commerce for instance, when Japan actually has so much advance regarding electronic payment variety and barrier to use.

On would-be-murderers, I am supposing they're not just different in their murdering intents, but also have different ideas, views of the world, and can deal with some situations better than the more obedient people. I'd see it as the best of both world if we could let them bring new ideas and try different things, while keeping active systems and arrangements preventing them from going to the dark side.

I wonder if Canada for instance is succeeding in this balancing act. I don't hate Japan as it currently is, but I think it stagnated way too long and it's becoming a bigger and bigger issue.

Murder rate is a compound of many factors of course. I'd see the ban on firearms and control at the frontiers as the #1 reason there's so few violent crimes. The worse incidents outside of organized crime ducking it out have been people running around with knives, and it that limits a lot the extent of crimes.

In comparison, european countries are more connected and the networks will be a lot more international. For instance Marseille has a kind of violent crime that comes from guns and drugs smuggled at the port that won't happen as much in Japan (Fukuoka is a city of its kind in that regard...)

On police presence, you'll see crime rate similar to Japan in well funded districts that have a very local and always present police. That makes them part or the everyday life, they will be more relaxed, more aware of the oddities and weird behaviors, and residents will also rely on them more as they are familiar instead of being some kind of alien presence.

Of course these cities will also probably spend more on school equipment, libraries, public infra etc. This costs money/taxes that not every city has or is willing to spend.