The (well-intentioned) mistake you're making is assuming US officials' top priority is the greater interests of America, rather than their own personal interests.
You could just as easily ask what the US gets out of the special relationship with Saudi Arabia, a country ruled by murderous tyrants, and the country of origin of the majority of the 9/11 highjackers.
In the cases of both Israeli lobby influence and Saudi royal's influence, the answer is money and power. Our members of congress are very easily influenced by "donations", and those two groups happen to be particularly wealthy.
On the flip side, the Mossad and many other intelligence groups are particularly good at getting blackmail material on politicians. If you don't play ball and you get in their way, they have the ability to ruin your career as well.
In my opinion, I would say the turning point where the US started to prioritize Israel as an ally was after the Suez Crisis. "In October 1965 Eisenhower told Jewish fundraiser and Republican party supporter Max M. Fisher that he greatly regretted forcing Israel to withdraw from the Sinai peninsula; Vice-President Nixon recalled that Eisenhower expressed the same view to him on several occasions." [Alteras, Isaac (1993). Eisenhower and Israel: U.S.-Israeli Relations, 1953-1960].
After Eisenhower's presidency, JFK further strengthened this alliance:
"As president, Kennedy initiated the creation of security ties with Israel, and he is credited as the founder of the US-Israeli military alliance, which would be continued under subsequent presidents. Kennedy ended the arms embargo that the Eisenhower and Truman administrations had enforced on Israel. Describing the protection of Israel as a moral and national commitment, he was the first to introduce the concept of a "special relationship" (as he described it to Golda Meir) between the US and Israel.[207]"
One exception was when JFK resisted Israel's efforts to develop nuclear weapons, which they felt was crucial in their survival as a country. "In a May 1963 letter to Ben-Gurion, Kennedy wrote that he was skeptical and stated that American support to Israel could be in jeopardy if reliable information on the Israeli nuclear program was not forthcoming, Ben-Gurion repeated previous reassurances that Dimona was being developed for peaceful purposes." You'll note that he was assassinated only months later. Not to get all conspiracy theory, but I've always felt the timing was a bit suspect.
Long story short, the US as a nation may not get much benefit from the relationship, but the individual politicians do. Until we get rid of the concept of lobbies, PACs, and require all campaigns to be tax-funded, politicians will continue to serve the countries and groups that pay them, not the American populace.