Well I agree with you, but they very much did want them. Iran provided a lot of funding for Project Flower and intended to use the technology to create their own missiles. Whilst this is destabilizing the region as you mentioned, I tend to believe that the US would side with the Iranians over the concerns of the Arabs, who quite frankly aren't the most trustworthy allies when compared to the Iranians. This could drive the Saudis into the arms of the Chinese who would have no qualms about giving them any sort of weaponry they desire.
You are correct, but the United States won't want anybody having nukes in that part of the world. The Saudis are highly unlikely to turn to the Chinese unless America gets to be seen as an unreliable ally. Otherwise, I don't think they'd bother, and even if Iran gets nuclear weapons, the United States may well be able to get the Saudis to calm down some. After all, the Israelis (who the Saudis despised more than the Shah in his day,
though Khomeini's wish to export his religious fanaticism changed that....) had nukes by the late 1960s. If the Americans are being power brokers in that part of the world, they may be able to prevent proliferation, particularly if Iran's government changes over time to something a little more reasonable, which would be a must if the Shah is to remain in control of the country in any form.
I think one interesting point is what happens socially to this Iran. I'm guessing that the end result eventually would be changes to the government allowing the Shah to give up more power to the Majlis, allowing them to make real laws but still giving him some control over the country. A sorta-democratic, oil-rich, industrially-developed and well-educated nation is the sort that can make real waves in the world in pretty much any area. Does Tehran do this? Does the Shah's dream of Tehran being a major center between East and West happen and if so, what does that do? If the nation can be a story of a highly-advanced, wealthy Muslim nation, does that change the perceptions of Muslims in the West, particularly after 9/11? Or perhaps the post-9/11 divisions between Shi'a and Sunni Muslims extend to the view of Shi'a Muslims being 'good' as opposed to others being 'bad'?
Being that with Iran on side the US can tell Pakistan to take a hike, does that improve relations with India? Does Iran's wealth and influence help the Palestinians? Or perhaps their Shi'a brothers in Lebanon or their friends in Syria? Does Pahlavi extend his wishes to help to Muslims in non-Shi'a nations?