A reader who knows a lot more about Middle Eastern foreign policy than I do writes:
Iran doesn't want and isn't planning to invade any country or even part of a country. It wants to become the regional "hegemon" in the Persian Gulf -- like the U.S. in this hemisphere or China in East Asia (which is China's long term goal) and Russia in the "near abroad" -- a role that a counterbalancing Iraq has prevented it from playing for many years.
Now thanks to the ousting of Saddam (and the Taliban in Afghanistan) Iran is able to reassert itself especially through the assistance of Shiite players in Iraq (and Afghanistan) and elsewhere. So we are not talking about the use of military power to occupy lands but more to affect decisionmaking in its neighborhood. Zbigniew Brzezinski described once what it means to be a "hegemon." It means that if the leaders of country X plan to pursue a certain policy the first question on their mind would be: How will the hegemon respond? I think that Iran, especially if it gains control of nuclear military power, will be able to achieve this goal and turn Iraq (or what's left of it), Saudi Arabia and the other Gulf states into its satellites.
You seem to play down the power of the Shiite revival as a major political asset for the Iranians (See Vali Nasr's important article in Foreign Affairs.) You write: "The basic problem, as far as I can tell, is that Arab and Persian Shiites are Arabs and Persians. They speak different languages, have different cultures outside of religion, and have different relatives." Arab nationalism is dead and there is certainly no "Iraqi" nationalism. So as Nasr and others (including moi) have pointed out: Shiite identity has become now a powerful force that can strengthen Iran's hands (in the same way that Pan-Slavism was a major asset for the Russians). As Nasr documents, some top figures in the Iranian leadership are actually Iraqis and vice versa; some of the "Iraqi" leaders are actually Iranians.
So ... things looks quite good for Iran these days and they've been very smart and cautious in pursuing their diplomacy. In fact, their major mistake will be to use their military power to attack anyone in the region. Like China in East Asia they just have to wait for the Americans and their allies to continue making their mistakes.
Now... I'm not proposing that the U.S. should therefore attack Iran but that it should try to do a Nixon-goes-to-China with them based on Realpolitik considerations.
Thanks. The big question then is what are the costs to America of Iran being a regional hegemon. For example, can they use this influence to drive up the cost of oil on the global market? Can they then turn higher oil revenues into a perpetual motion machine where increased oil revenue is turned into weapons or less violent foreign influence, which drives up the price of oil higher?