There should be equality in society as a matter of justice. Hierarchy only benefits those at the top, and creates hostility between those at the bottom and those at the top. This can result of conflicts and uprisings. Also, those at the top still have the risk of falling from the top.
Yes, we should be pushing to make things equals for everyone in the world, let alone the United States of America. People need to realize that God has created all people as equals and it's important that we pursue that same goal in our everyday lives. No equality is a sign of a weak nation.
I believe it is more beneficial for a society to strive for equality, even though it generally balances out to some kind of hierarchy. I think setting the goal at hierarchy simply gets us where we are currently at. You have 1% that controls almost everything. That doesn't help anyone, we should also seek equality, even if we don't meet the goal.
Yes, it is more beneficial for a society to strive for equality, because the people who think they are better than everyone else will take advantage of their position and they will live off the people who are the least powerful. That will lead to discontent and ultimately to civil disobedience and possible war.