The military base is there to protect the regime. It’s easier to deal with a small monarchy with no transparency than a democracy. And they make for a good enemy of other local countries keeping just enough zest in the region for the weapons to keep flowing and the figureheads to keep toppling, but still allowing for a steady supply of oil.
History of Modern Middle East by William Cleveland is a good resource:
When people have democracies, they start asking for crazy things that are in their self-interest, such as mineral rights and ownership over their farmland.