Iran is the strongest state by far in the Gulf region. If the region (and I'll consider Israel out of the region for this purpose) remains non-nuclear, Iran will be the dominant local power. Throw in nukes and Iran's influence is blocked in theory. Press too hard and somebody else might lob a nuke at them.
Iran will not be the last Middle Eastern country to go nuclear if we don't stop the mullahs:
Officials and opinion leaders on the west (Arab) coast of the Persian Gulf are talking openly of using a chunk of their oil wealth to buy nuclear weapons, if Iran gets them. This would be a defensive move, to defend their oil from Iranian aggression. The Iranians have been the aggressors and empire builders in the neighborhood for most of the past five thousand years. Arabs have long memories, and few of the ones that involve Iranians are pleasant. If Iran remains without nukes, the Arab oil states are not going to spend billions of dollars, and lots of favors, to buy nuclear technology. But if Iran has nukes, they will more likely be aimed at Arab oil, before they are pointed at Israel. The Arab oil can't fight back, unless the Arabs have nukes, but the Israelis can, and there is no doubt that they will.
The Arabs could offer a huge amount, in cash or oil, to buy nuclear weapons technology. While the UN, and nations, would protest, none could fail to see the economic logic of protecting your major asset.
We'll need a new meaning for MAD should this happen. How does one have mutual assured destruction when a simple dhow can pull into a port and go mushroom cloudy?