What makes you think that it's not already like that for certain classes? Income mobility is historically low. Also why would people grow comfortable in their poverty? What exactly does that mean? That they've made peace with the fact that they have to choose between being dead or being broke? As long as there is poverty there will always be complaints.
Go to a poor country. See how people go about the days. It's as if there is a "place" and people "know" their place.
If you don't believe in having a stationary "place" you seek more, you tell your progeny there is more, if only they try. Go, don't be like your father or mother, go make something of yourself.
Just because you don't believe in a stationary place doesn't mean you don't have one. Plenty of people may believe in the American Dream but that doesn't mean it's real. Plus even if you don't believe in upward mobility it still doesn't mean you're happy where you are. Shitty conditions are shitty conditions regardless of whether or not you think you can get out of them if that's even possible.
Imagine, there is no dream. You get what you have. There is no chance for anyone who has not achieved. Don't even try, there is no chance.
I think we'd be worse off with that mindset. I imagine Russia, Venezuela, etc. feel a bit like this. You're there to eek out a living with little chance of thinking things could change for you.