The political system doesn't want it... rich people and corporations want it. They control the political system. Money is speech after all.
I agree that poor left people and poor right people have a lot more in common than poor right people and rich right people. However, like you said, if they turn us against each other then we won't go after them.
I'm going to have to go ahead and agree with 99 about the false equivalency to be honest. If you want to talk about opinions and interpretations then that's fine.. everyone thinks they're right but when it comes to actual facts and reality... just their existence.. then it's not a case of "both sides are doing it". Not in the slightest.