Accepting that we have classes here in the US and telling people that they are in some way stuck in their particular class are two very different things. I would never make the assumption nobody is capable of rising above their current "station," either socially, financially or other--nor would I assume the impossibility of the powerful falling from grace. I believe that the possibility of mobility within the classes is what sets us apart from other societies. I believe it is one of our country's greatest strengths. I believe it is why immigrants flood our borders from every nation on the planet, and comparatively few clamor to leave. Does that mean our class system is always 100% fair? Is it ever taken advantage of by the powerful? No and yes. But it is a fact. As I stated, as long as humans are social creatures, we will have classes.
Additionally, it is true that when one feels chained to their particular class he is likely to become depressed, desperate, even violent. My experience, living in an inner city since 1993, has shown me that the urge to rise above is far more common than the acceptance of chains.
In the United States, we have a class system "where social rank is defined in terms of wealth and income. There is movement between the classes. This system is an open system and there is social mobility. (Understanding Sociology, Basirico, Cashion, Eshleman, Barlow and Holley)." We do not have a "Caste System", which is given to a person at birth and is a closed system.
About the only place you'll find an almost classless system is in Hunting-and-Gathering societies where there are usually less than 50 people total.