Perhaps Cheney thought that invading Iraq the second time would increase stability. The effect was, however, the opposite. The incompetent aftermath of the Iraq II war gave birth to ISIS and massive instability in the Middle East. Hundreds of thousands more people died because of this instability. The fall of Saddam Hussein strengthened Iran, which went on to arm the Houthis, Hamas and Hezbollah.

As to oil prices: the countries in the Middle East that have oil need to extract it and sell it. Whether they are the Saudi monarchy, the Iranian theocracy or Saddam's repressive dictatorship. I'll note that Saddam also wanted stability, since he wanted to remain in power.

What Cheney was probably trying to preserve was access to this oil by US oil companies.