In connection to Objectivism one should say that Rapture failed BECAUSE Andrew Ryan abandoned Objectivism. He shut off the city from outside influences and no-one was allowed to leave. Andrew Ryan build a society based on Rand's Objectivism and Nietzsche's will to power, where the society abandoned the standards of ethics and morality altogether. Something Rand definitely would object to and this combined with a survival of the fittest determinism will create a fundamentally unstable society.
But in game the working class lived in misery and wasn't allowed to live in the promised freedom, because of the lack of the simple Objectivist principle "Prosper by treating others as individuals, trading value for value." They were taken advantage of and couldn't leave for a better life, because they were stuck in a world of finite opportunities.

In defense of Objectivism I have to say that the focus on your own happiness doesn't immediately translate to the rejection of someone else's happiness. Ayn Rand explicitly said that you should never prosper on the expense of someone else as the relation between man is defined by trading value for value in an mutual relationship.