There are many reasons why keeping Iran as an enemy would be beneficial to the U.S. In a game of geopolitics, especially when you're a superpower like the U.S., the end game isn't always "let's all be friends". Enemies, real or imaginary, can be very beneficial.
There's just so many variables. We'll have to see how this plays out.
Well, the main problem was that the USA under Carter - who should accompany Dubya in the worst of the worst lists - put itself in a very awkward position: Due to the Islamic revolution, Carter stopped backing the Shah. This was crucial to the success of the Shah's overthrowal, as Mohammed Reza Pahlavi was very ill, and it was believed by the Iranians that he would die soon. Since the USA ceased support of him, the Shah's Iranian backers in the military flip-flopped towards Ayatollah Khomeini, as they felt that their alliance with the Shah would have no benefit anymore - they would if they could count on US support.
However, this all happened without the USA shedding the reputation of backing the Shah. Now, the ayatollah already had an irrational hatred of Israel and the US, but even if he wanted to become friendly, the reputation of the USA as being a backer of the Shah meant that he would destroy his domestic reputation if he rapproached with the Great Satan. Carter deservedly was kicked out of office, and Ronald Reagan tried to compensate for the mess Carter left by laying the foundations for the US-Saudi alliance, which marked the final nail in the coffin for any possibility of a US-Iranian rapproachment in the foreseeable future, back then.
However, the US-Saudi alliance is a very unnatural alliance that shouldn't have existed. It's an inheritance of Jimmy Carter's incompetent and ******** foreign policy. Saudi Arabia is hostile to Israel and its regime bases its domestic legitimacy largely on that issue. Iran, with it's hostile Arab neighbours, would otherwise be a natural ally of Israel, and important Israeli figures like Ariel Sharon rightly perceived that, supporting arms deals with Iran in the 1980s to help Iran fight against Saddam Hussain (that's right, after the Islamic revolution).
Now Iran's Anti-Zionist allies have become hostile to Iran itself due to religious differences (Hamas) or being bogged down in a hopeless conflict (Assad & Hezbollah), which is ending the last moral commitments Iran could possibly still have against Israel, this in addition to the fact that large segments of the Iranian populace is sympathetic towards the US. Perhaps, the current Ayatollah allowed to happen the end of Ahmadinejad's presidency just for the current rapproachment to happen. Which would be a good thing, and allows the USA to finally put an end to the horrible alliance it has with Saudi Arabia.
(note that I mentioned Israel a lot of times in this story, as the USA's disposition towards Iran can't be seen without involving Israel either: Israel is too popular among the American public even without the Pro-Israel lobbies, and given Israel and the US have plenty have common enemies and common concerns, it is much better for the US to have another ME ally that - in the current geostrategic environment - has no innate interest to be hostile to Israel. Iran would be that ally.)