I don't think this is true across the board. In my experience, the broader culture can make a huge difference.
For instance, like many others, I was bullied every single day in middle and high school in the US. When I moved to NZ and went to high school(called "college" there), I was dumbstruck at how accepting people were of me, as someone who has been constantly bullied back in the US, that I had a hard time accepting it at first. I was so used to being an outcast that I didn't know how to handle it at first when normal kids would actually approach me in a non-confrontational way. By the end of the year, the most popular guy in the school was voluntarily helping me study for chemistry.
Now some of that experience may have been influenced by me being a foreigner, but my bullying was due to a combination of being nerdy and fat, so it would have made sense if at least some people bullied me in NZ. There was pretty much only one kid who didn't like me and had to make a show of it, but he was easily handled.
Put simply, I think that culture in the US and probably other western countries that are heavily US-influenced is woefully broken, but it isn't as apparent to the conscious mind because we've become very good at polishing turds. We love to paint over rot and create rules for ourselves that just sweep problems under the rug so that they only manifest in places out of our control, such as with the interactions between children.
To your point, though...
> Instead they spend all their time with other kids who are have they exact same emotionally immaturity as they do. You get feedback loops of bad behaviour, and put them in bubbles where their peers and their psychopathic games (like bullying) make up 100% of their reality.
This is true in more ways that you might have originally imagined. Young people, and really people of all ages IMO, should be learning from their elders. Instead, we put way too much emphasis on mere socialization and compatibility. In adulthood we're even worse in these categories in that we either socialize too much or too little, and fewer of us will tolerate anyone who doesn't tick off all our arbitrary boxes.
> The only consistent counterpoint I can think of are cousins, who are typically slightly older or younger, and are outside of kids' normal peer groups. As a result these are often very positive relationships.
Cousins, unlike siblings, aren't competing with their fellow cousins over the love of their own parents, so it makes sense that these relationships tend to be positive.