By this second definition, a country can definitely be rich across the board without having a “poor” second class. Just make sure people earn a decent living wage, and then some. There will be low crime (no need for gated communities!), high trust (no need for a lawyer on retainer!), and good education and health care (no need for private schools or hospitals!)
You have a very zero-sum view of wealth, the idea that to be wealthy means it’s gotta be to the detriment of others. I’m not saying Norway’s got it all figured out, but they’re definitely gunning for something closer to what I describe than what you do.