Thing is, study after study has shown that people's happiness depends not so much on their absolute well-being, but upon their relative well-being.
The clearest example I can think of is a study the U.S.Army did in WWII. The brass was worried that morale for black soldiers would be worse for those on bases in the segregated south than in the north because of the added social restrictions they faced there when they went on leave. Objectively, black soldiers stationed in the north were better off than those stationed in the south. Turned out that those soldiers didn't base their happiness on what happened to themselves alone. Those in the south had higher morale than those in the north. They compared their lot to that of southern black civilians and felt pretty good about their lot because it was much better than their comparison group. Conversely, the economic opportunities the war brought northern black civilians meant that black troops stationed in the north felt they were worse off than those they compared themselves to, so their morale turned out to be lower.
Thinking on this, I now realize why class stratification tends to occur. It gives everyone except those in the lowest class a chance to feel better about themselves than they otherwise would, simply because they are in a better class. So long as one can keep that lowest class small, class stratification might actually be an overall good for society, if happiness is your measure of good.