There are a lot of actions the United States wishes its string of pro-US dictators would take that have been denied. Egypt's Mubarak did not build an underground wall as quickly as Israel would have liked. Palestine's Abbas does not come to the negotiating table without an Israeli suspension of construction. Saudi Arabia's dictator Abdullah does not recognize Israel.
The indirect rule of these countries, Palestine's West Bank, Egypt, Jordan, Saudi Arabia, Kuwait and UAE by the United States is enforced by threat and in the cases of Egypt and Jordan by direct bribery, but none of these leaders acts as a part of any US chain of command. Along with torturing its own citizens who display tendencies to oppose the dictatorship, Jordan arms and trains troops to fight Hamas, it tortures suspects on behalf of the United States and it sends translators to assist the US in ventures in places that speak Arabic. For this it is rewarded likely with payments and opportunities directly to Abdullah and his family and with some economic and military benefits designed to strengthen his hold on power in his country.
But how far would he have to go before the US would make its constantly underlying implicit threat explicit? Before the US begins a serious search for an alternative Jordanian ruler who would be more compliant? There is a trade-off and Jordan's Abdullah does have some freedom of movement. On the other hand, even US military personnel in actual chains of command have some freedom of movement. There is an amount that one must overstep before replacement or punishment becomes a consideration even under formal organizational hierarchies.
If Jordan's Abdullah spoke out against the attacks on and starvation of Gaza the way Erdogan does, he would not be replaced the next day. But the US ambassador would express his anger, some benefit would likely be withheld and contingency plans for what to do if Abdullah goes further would be re-examined.
There is a balance. The US would like Saudi Arabia to make concessions to Israel in exchange for Israel suspending construction. The US has surely attempted to present a list of benefits that the Saudis could be offered, and nothing on that list was compelling to Abdullah. The United States is not sure that it could find a replacement Arabian leader who would make further concessions to Israel, and the risk of a bad outcome is too great for only a symbolic benefit.
However, the Saudi Abdullah making the US ambassador angry would begin to set in motion events that if Saudi independence continued, would make the US more indifferent to threats to the Saudi throne.
It is a balance. It is not nearly the balance a democracy accountable to the people ruled would strike, but Saudi Arabia is not ruled the way it would be if the US ambassador sat directly on the throne. It was a late colonial-era advance in which indirect rule began to be seen as preferable to direct rule only because a native figurehead on the throne inspired fewer attempts at rebellion. The British decided that some degree of freedom for the figurehead was worth the reduced cost in maintaining the rule, and the Americans today in their indirect rule of the region are following the same practice.
On important matters, Jordan's Abdullah, Saudi Abdullah, Egypt's Mubarak, Kuwait's Sabah and the UAE rulers have to submit. Any would be replaced if, for example, they attempted to break Israel's monopoly of nuclear threats, they offered anyone training such as Iran offers Hezbollah that actually can be effective in resisting Israeli advances or even if they attempted to introduce popular sovereignty to their countries - giving control of policy, especially of foreign policy, to any decision-making process in which the public has direct leverage.
On symbolic matters, these puppet rulers strike a balance between the direct rewards the US can offer and the cost cooperation with the US and its unpopular project of maintaining a majority state for 5 million Jewish people imposes on their own legitimacy.
