Funny how the whole agenda for the region is set by Israel and not the US themselves.
In regards to game theory it's better for the US to have Israel as an ally and make an enemy of Iran than the opposite. Don't forget that Israel has nuclear weapons and the country would not hesitate to use them in self defense. Also while the Saudi's are scum, you'd have a situation worse than Iraq if you removed them from power.
In the end there's no great answer, just one that has a not as worse outcome.
I'm not sure I'd call Israel a "true friend." At a high level they may be ideologically aligned with the West, but they're simply using the USA to advance their own interests.
Pakistan also has nuclear weapons, Israel's use as such is probably mutually assured destruction, not 'self-defense'.
Developed independently of the US[1], in cooperation with the apartheid government of South Africa. South Africa went on to become the first (if not only) country to voluntarily give up it's nuclear weapons program, right on the cusp of black rule.
Officially, the US does not/will not acknowledge Israel's nuclear capability.
Since there is oil, the US needs reliable partners. Saudi Arabia (totalitarian regime with an abysmal human rights record) and Israel (actively engaging in war crimes and apartheid) are the best America can manage.
Saudi Arabia has more money than they know what to do with, and they're easily placated by selling them advanced weapons. Israel is on a much tighter budget and is more militarily vulnerable so they need a lot more help. That they've pissed off everyone in their immediate environment doesn't help, either.
Sadly, pre-revolution Iran and pre-civil war Lebanon were vibrant, flourishing countries. Then some geo-political meddling went down and here we are, a total mess.
The US was initially a reluctant ally with Israel. The Soviet Union was actively arming Israel's Arab neighbors and fanning the flames of war to win influence with oil producing Arab states. At the same time the US had embargoes on selling arms to Israel because it was reluctant to fan the flames of war and also to antagonize Israel's Arab neighbors.
Unbeknownst to the US Israel had developed a nuclear weapons capability and at the start of the Six Day war Israel felt threatened enough to deploy them. In what must have been an interesting phone call Israel informed the US both of their nuclear weapons capability and that they were going to nuke Cairo. In order to dissuade Israel from this course of action the US promised swift delivery of modern anti-tank weapons and depleted their Western European inventory of these weapons. This helped turn the tide of the conflict and reduce potential of a nuclear exhange in the Middle East.
The result of the Six Day War was that the US committed to keeping Israel at par with its Arab neighbors conventional military capabilities if Israel would keep its nuclear capability in check.
A great writeup of the history is here:
http://www.au.af.mil/au/awc/awcgate/cpc-pubs/farr.htm
This still plays an active role in the US and Israeli relationship and was even a factor in the negotiations over the Iranian nuclear program but the nuances are rarely picked up by the US press.
Israel also plays an outsized role in US politics because it is an influential issue with Jewish voters and also, oddly, Evangelicals. Evangelicals see the establishment of a Jewish State in Israel as a prerequisite to the rapture and the Second Coming of Jesus Christ.
Great article on how the delicate compromises in the Middle East were almost toppled by a cow:
http://www.pbs.org/wgbh/pages/frontline/shows/apocalypse/rea...
Also there was no need for Israel to use it's nuclear weapons during the Six Day war, it destroyed the Egyptian Air Force within the first 5 hours of the war.
I think you are confusing a lot of "facts" here, your story might fit more with the 1973 war, but during that war if were the soviets who've actively moved theater level nuclear weapons into Egypt and the US had put pressure on Israel to stop it's advancement.
Overall if you read slightly better sources you would see that the Six Day war actually pushed the Israeli weapon program back, France have stopped the cooperation with Israel and the knock-out victory that the Israelis have dealt to the combined forces of Egypt, Jordan and Syria as as gaining control over the Sinai Peninsula which meant that Egypt can no longer blockade Israel as it lost the controls over the straits of Tiran made the need for a bomb not as urgent.
The nuclear program has really stepped up after the 1973 war both because Israel decided that the added geographical depth of the Sinai wasn't sufficient and because the Soviets have actually pushed weapons into the theater which meant that Israel needed a MAD option and quickly.
For those who don't want to wade through the bulk of the material (which is still fascinating) the relevant history begins is Section III of the document and relevant sections condensed below:
Defense Minister Moshe Dayan, obviously not at his best at a press briefing, was, according to Time magazine, rattled enough to later tell the prime minister that “this is the end of the third temple,” referring to an impending collapse of the state of Israel. “Temple” was also the code word for nuclear weapons... The Israelis assembled 13 twenty-kiloton atomic bombs. U.S. Secretary of State Henry Kissinger was notified of the alert several hours later on the morning of 9 October....
Israeli commandos flew to Fort Benning, Georgia to train with the new American TOW anti-tank missiles and return with a C-130 Hercules aircraft full of them in time for the decisive Golan battle. American commanders in Germany depleted their stocks of missiles, at that time only shared with the British and West Germans, and sent them forward to Israel.
Thus started the subtle, opaque use of the Israeli bomb to ensure that the United States kept its pledge to maintain Israel's conventional weapons edge over its foes. There is significant anecdotal evidence that Henry Kissinger told President of Egypt, Anwar Sadat, that the reason for the U.S. airlift was that the Israelis were close to “going nuclear.”
The timeline of all of these events do not make any sense and are with odds with official declassified Israeli and US documents.
The TOW missile part is especially humourous.
P.S. By the time the first US airlift has landed in Israel, the Israelis have already broken through the Egyptian lines, the 2nd Egyptian army was surrounded and cut off and the Israelites crossed the Suez canal. Overall the reason the US agreed for the airlift was because the soviets were already running airlifts into Egypt and the US did not want to risk the soviets deciding to commit troops (well other than "advisers").
Recent declassified documents about the CIA briefings to Nixon also show that the Soviet actually transported nuclear material into Egypt during the 1973 war, this was what put the US on high alert, and it's also the reason why they sent their SR-71's over Israel and the Sinai and the pressing the Israeli government to hold their advance or they'll release the photographs to the UN. http://edition.cnn.com/2016/08/26/opinions/secret-briefings-...
"...win influence with oil producing Arab states..."
Yeah, nothing to do with oil.
It's all about oil. That whole area is about oil. A case could be made that World War I was about oil, that British naval supremacy depended on it, and everything since then is a mostly direct cascade from that.
Also don't forget that the extreme Evangelicals believe that the establishment of and subsequent destruction of Israel is a necessary precursor to the Rapture. What a psychotic viewpoint.
"...for reasons that have nothing to do with oil"
"...win influence with oil producing Arab states..."
Stability is only a concern because of the critical suppliers there. Notice how little interest is paid to places like central Africa where, apart from Nigeria, there's no productive oil fields.