The US had no problem providing Saddam with money, arms, and biological weapons in the 80s[1], even after he used them against Iranians. And of course, the US been involved in Iran since 1953[2] when they overthrew their first and only democratically elected PM because he wanted to nationalize their oil reserves. As long as Saddam massacred the "right" people, the US fully supported him.
As far as instability, the very boundaries of Iraq were purposefully drawn so that the Kurds, Shias, and Sunnis would be locked into the same nation state and easier to control. Saddam was just one of the pawns in the great oil game the US and the western world has been playing there. The fight over access to oil - the singularly important resource that enables modern armies and economies to function - is the underlying cause of the instability in that region, and has been for the last century.
As far as instability, the very boundaries of Iraq were purposefully drawn so that the Kurds, Shias, and Sunnis would be locked into the same nation state and easier to control. Saddam was just one of the pawns in the great oil game the US and the western world has been playing there. The fight over access to oil - the singularly important resource that enables modern armies and economies to function - is the underlying cause of the instability in that region, and has been for the last century.
[1] https://en.wikipedia.org/wiki/United_States_support_for_Iraq...
[2] https://en.wikipedia.org/wiki/1953_Iranian_coup_d%27%C3%A9ta...