Greed is not a problem, the desire for more has led to every breakthrough and innovation the world has ever seen. Somebody saying "I can do this better than you" has created every improvement in man's history. And greed has always motivated that statement.
The answer to this question is so obvious that everyone is overlooking it.
The biggest problem today is a belief in the supernatural. From this flows the belief that some people are "better" than others, which leads to the stratification of societies, wars, and a belief system that, even when "under the surface" remains resident in our leaders and in government.
Governments, problem causers that they are, are that way because their leaders (like most people) cling to a belief in the supernatural.
The supernatural means many things to many people. The Jesus cult, Islam, and Judaism are the big three of monotheism, and Judaism differentiates itself slightly by not seeking coverts and by denying life after death.
Eastern belief systems like Hinduism have enslaved hundreds of millions, and the Buddhist belief in karma is another example of this stupidity.
Almost all violations of human and property rights can be traced to a belief in the supernatural.
Until science proves our origins and discredits the supernatural entirely, man will remain chained to a belief system centered on death; all of them are this way as death is universally seen as some sort of gateway to this supernatural realm.
Save man! Destroy god.