About history. If you back up time, say a thousand years ago, and look at the world, what do you see? Or how about two thousand years or further back?
Over a thousand years ago Europe wasn't worth invading- serfs, dirt poverty, unenlightened, robbery, warfare, etc.
About Politics. The politics in Africa is typical and the norm. The exception was empires which would rise then fall. America is very different, and it has transformed the rest of the world. You are living in a very thin slice of time, which over the longer term is uncertain.

As far as Africa being a cesspool. Well, first you should realize that it was one the battlefields in the Cold War. Next, even if our various aid program weren't full of corruption, they aren't based on workable plan. Welfare programs are fine, if you are focused only on the short term, but their needs to be more fundemental changes, which these welfare programs can actually hinder. What Africa needs is trade. It needs land ownership which encourages modern farming. It needs foreign investment. [America was built on foreign investment.] But the hardest thing is the the people have to want to change. The second hardest thing has to do with bigotry- white and black bigotry; and religious bigotry.
Of course at the moment the biggest crisis is the Aids epidemic- which is properly a welfare type program. We are living in a world which requires advanced medical technology. Africa needs a quick fix in regards to Aids, but it also needs fundamental change in it's general economy and accompanying improvement in medical care, so as to prevent it from remaining a potential source of new diseases which could threaten the world.