"It ain't what they call you, it's what you answer to." - W. C. Fields
Now we have the worlds largest so called US EMBASSY in Bagdad that cost over 5 billion dollars to construct, contains over 600 buildings that house about 15,000 US personell (most of which are private and US state military personell and spies)
A bit of an overkill for US tourists travelling through Iraq wanting a passport replacement dont you think?
And lets not mention the oil exploration licenses in western Iraq that were almost entirely tendered out to US and some minor western Oil corporations. (thats if you wish to call it a tender process)
I'm not sure how you think nations with nuclear weapons behave, but the prevailing doctrine in both academic and strategic literature and policy analysis is a litany of references to the strategic implications of a nuclear weapon state and how such capability augments the capacity of a country to behave assertively and forcefully within its periphery and abroad. The most highly cited example in history is that of the US and USSR for obvious reasons. Moreover there are plenty of contemporary or near past examples to examine. I'm not sure what you are getting at. This is not a discussion of MAD, that is a separate issue and a valid one.
Furthermore you have missed my point. I'm not saying Iran would pass along chemical weapons to Hezbollah, that probably would cross a redline even if the state had nuclear weapons and would incite a like minded retaliation. The issue is that Iran has consistently, since the 1979 revolution, sought regional hegemony with a religious-nationalist tint. In pursuit of this it has incited and attempted to foment rebellions in Saudi Arabia and along the Gulf littoral, it has battled for control over the future of Iraq in the hopes of winning another firm ally, extended ties to the Houthi rebels of Northern Yemen as a possible conduit for Iranian power to upset Saudi power in Yemen and Najran and Asir, it has pursued the creation of strong proxies in Lebanon to balance against Israel and to assist in the cementing of power with Syria, and of course it has funneled weapons and aid to Hamas as a means to counterbalance the GCC backed Palestinian Authority, etc etc.
A nuclear weapon would significantly reduce Iran's reasons for limited its assistance to these groups and in restraining its activities abroad. Why? Because a nuclear option no matter how weak massively reduces the prospect that a Western or Gulf coalition will strike back at you. It adds a tremendous layer of doubt to every possible conventional or unconventional encounter.
They seem to love him in Iran