I would not characterize it as greed.
Not that greed isn't involved, it just seems to miss the point.
Currency has become so universally trade-able, and everything so reliant upon it, that it has become capital in and of itself, and the potential for it to be used (invested) has become it's principal value, which results in people trying to create value by allocating it to the right places (and capture the created value for themselves, obviously). The issue arises when the whole process is so obscure and hard to figure out that it becomes a breeding ground for people who are effectively swindlers. Moreover, when money=power=status, the typical means of correcting defective behavior, from an evolutionary standpoint, fails, as reputation losses can be overcome easily as long as you retain wealth. Likewise, as it serves as a lever for power, and is a more effective lever the more different types of power it can be translated into, wealth sustains itself and tries to prevent it's own confiscation. Add to that the 'taxation market' that drives taxes down on the rich who can move at leisure, and you have issues for anyone who isn't already there. It is not impossible to become rich, it's just really hard, and requires more than just work; it needs luck. Luck for something to not go wrong as much as luck for something to go right.
It's a cultural construct I suppose, but so are group dynamics and familial interactions. I look at it like an ecosystem or organism or what-have-you. It follows certain laws as a tendency (not a hard rule), but these laws interact with themselves and each other and are complex enough that it can be really difficult to figure out which levers to push and how hard they need to be pushed, especially with how intimately it interacts with human psychology.
It's meant to serve as a way of allocating resources effectively when there's not enough to go around perfectly. Which means when there is enough, and it's a necessity, it runs into problems.
We do have wage caps on CEOs, I believe, there's just no cap on bonuses. I figure that past a million dollars a year, personal income can be taxed around 95%, and that bonuses shouldn't be higher than your annual salary.
Debt-based economies are rather fragile, unfortunately. >.> I would very much like to see several aspects of Islamic banking practice become the norm.