It was not the US that perpetrated the violence after it toppled Saddam. It was the radical elements within Iraq. They're the ones that bear responsibility.
There is a reason why Kurdistan is one of the most peaceful and developed regions in the Middle East: they act the way you must act to be a prosperous modern people. The violent radicals who squandered the post-Saddam opportunity to build a modern Iraq are to blame for the killing and the chaos.