Hobbes made the observation back in the 1600s that humans feel that they are fundamentally equal to one another, and as such they believe they are all equally deserving of the same things; as a result they want to take from those in positions of power so that they may make themselves equal. While the whole "people think they are equal" thing is up for debate, it certainly appears that Rapture fell because of the simple fact that you cannot take people, no matter how enlightened, from a capitalist, consumerist, and by design competitive society, and then tell them "you may be unequal, but this is the part you play; deal with it". There is a character who remarks that "someone still has to clean the gutters" or something to similar effect, and that essentially sums it up right there. Rapture was already falling apart before Fontaine and Ryan's conflict; they just sped it up by taking advantage of the situation for their own respective ends.