Of course there are a wide variety of cities on these continents, and I cannot even begin to express that variety in a short forum post. Cities will have a mix of wide streets and narrow streets in different proportions, and we can have great debates about what the right proportion ought to be. And yes, architecture and design can work together to overcome the negative effects of width -- up to a point.
But there's really no way around the fact that the typical South End residential street is really too wide:
That's a whole lot of open pavement, surrounded by storage for automobiles. That's a race track, not a street for people.
Compare that to this narrow street:
Acorn Street, Beacon Hill.
(Fun note: it is said to be the most photographed street in all of Boston.)
Most of Tokyo's streets are small like this, not just one. It's easy to find them. Yes, Tokyo also has giant streets, elevated highways, and all sorts of craziness. A city can (and should) have both small streets and big streets. I think it's telling that Japanese parents don't mind letting their kids walk around on these small streets. Just because the street is in the city doesn't mean that it shouldn't be safe for kids. In fact, I would argue, streets in the city ought to be much safer than the ones in the countryside. We shouldn't have to banish cars completely (really, not desirable or possible) in order to have such safe streets.
Japan is also, quietly, one of the top bicycling countries in the world. For the same reason: it's pleasant and safe to be in most Japanese cities without a car.
I understand your fear of letting kids play on any street in the United States. I think it's unfortunate, and a sign of how far we've fallen. Within my lifetime, we've gone from letting most kids walk and bicycle to school (myself included), down to having almost no kids walk and bicycle to school. That's a travesty. The big advantage of growing up in a city like Boston should be the freedom to wander the streets. If you aren't allowed that, then what's the point of living in the city? If you're going to be trapped in your home anyway, may as well make it a large home out in the suburbs.
Sadly, I believe that many families have made that choice for exactly that reason. (on top of other issues, which I won't get into).
Upton Street is 3 lanes wide, making it slightly too wide to be considered a narrow street. Now, if it were treated better, perhaps it could function as one. But it is not treated well, it is just used for automobile storage for the most part. Not a place for people.
West Newton Street is typical of South End streets, and that's what I'm talking about. Like the street in my picture above, West Newton is 4 car-widths wide: that is not a narrow street. It also happens to be a main through-route, so perhaps it is appropriately sized. That's fine. We need some through-routes. But the problem is that most every other street around it is also similar in size to West Newton Street, even the ones that ought to be small residential streets. That's the problem I have with the South End.
Well, I'm entitled to my own opinion about the South End, and so is everyone else. But we need a common language. If streets like West Newton Street are labeled "narrow", then that label loses all meaning. What's the point of doing that to ourselves?