Israel’s influence, while mighty, is not the basis for US actions in the Middle East. Control of oil, geography and establishment of military bases determine US policy. Israel and Saudi Arabia are useful tools for the oil and financial monopolies. Israel and the Saudi royals work on behalf of US imperialism. Destroying secular nationalist governments, supporting US friends, invading US enemies, supplying terrorists, assassins, money, weapons. When open aggression by the US needs to be avoided, the US can rely on Israel and the Saudis.
See for example Noam Chomsky:.
Jeff Halper, at the end of a long essay bullets why Israel is so useful to the US. “Israel’s military influence as a point-country for American Empire stems from four main sources:” See