I wouldn't mind Americans pushing for war in Iran if they were able to articulate a coherent policy reason for doing so. Seriously; if someone cheerleading an American war (proxy or otherwise) can explain how they think American foreign policy interests will be substantially improved in any way by regime change in Iran, I am all ears.
Without even delving into how America has bungled many earlier interventions in the Middle East, lets focus on the most recent shitstorm; Syria. America was never going to win in Syria, despite being by far the most powerful actor involved in the conflict, because they wanted something impossible; the removal of Assad AND the defeat of ISIS. Both of those things couldn't happen because by the time the USA got majorly involved there was no other significant local actor other than the Kurds who wasn't supporting either Assad or some form of genocidal Sunni rule.
America couldn't thread that particular needle, because ISIS was so cartoonishly evil that even though America's stated goal in the beginning was the removal of Assad from power, they couldn't stomach the only obvious force in a position to take him out; namely, ISIS. The idea that there were ever 'moderate' groups of any particular importance on the ground was a stupid pipe dream.
So Iran and Russia, because they actually had a clear goal in Syria (protect their proxy, Assad), accomplished this goal pretty handily.
So, that said, lets look at Iran. An important thing to note about Iran is that the country is mostly Persian, and mostly Shia. There are minority populations of Azeris and Kurds. There are very few Arabs, and very few Sunnis. Most people speak Farsi, not Arabic. The terrain is also fairly mountainous.
So right off the bat, everyone should understand that what OP is proposing--that a force of soft-ass Gulf Arabs are going to occupy Iran--is bugnuts crazy. Local populations do not respond particularly well to occupation by people who are a different race, religion and language, and Shia Muslims love martyrdom like nobody's business. During the Iran-Iraq war in the 1980s, Iran would send waves of unarmed young men running ahead of their attacking forces to clear the Iraqi minefields for their attacking forces. These people do not fuck around. The hardcore Shia live for this shit; if you picture Waco but with the martyrdom turned up to 11 you will have some idea of what to expect if you put the Iranians' backs up to the wall.
So lets say that America gets involved in a big way and carpet bombs the Iranian regime into submission, and sends in troops to take Tehran. I have zero doubt this is possible, even with Russian air defense systems being used by Iran, because America's air superiority is overwhelming and a middle power like Iran, even with serious support from Russia, cannot hope to compete with America's ability to project force. So America wins handily, maybe even with minimal casualties, the same kind of cakewalk as Iraq.
What then? Iran isn't going to turn into a sectarian shitshow like Iraq or Syria, because they are mostly Persian, and mostly Shia, in the core of the country especially. So you are likely to deal with a very aggressive insurgency focused like a laser on maximizing American casualties, without the distraction of murdering each other, like in Iraq and Syria.
And how do you extricate yourself from this problem? You can't liberate Iran. There is no way, zilch, zero, of installing a pro-American democracy in Iran, because the majority of the country, especially the hicks in the sticks, actually support the regime, especially if the alternative is an American puppet. So if you actually let them vote, they are going to vote America out, and probably bring in some kind of kind of government which hates America with every fiber of its being. Which leaves the option of installing some sort of pro-American autocratic ruler, like a Shah or someth-. Oh wait. I think I know how this story ends. I know, I know; 1979 is long ago, it is easy to forget.
You could also do the traditional British imperial thing, and pick some minority population and put them in charge of basically everything, so they are totally dependent on you, and then use them as a proxy to control the country. I don't see this working particularly well either, for a couple of reasons:
1) America has traditionally been absolute shit at this sort of traditional empire building, because it is too raw an exercise of realpolitik to square with the American public's view of itself;
2) There isn't a large enough group that America could hope to put it in charge of the Persian areas of Iran and hope to hold them for any length of time; and
3) Even when you are good at this, the way the British were, that sort of setup tends to play out with massive ethnic cleansing and/or genocide a generation or three down the road. See Rwanda as an example: the Belgians put the Tutsis in charge of the Hutu, and well, the rest is history.
America just doesn't have the stomach for the losses that a longterm occupation of Iran would cause, and the Iranians and everyone else knows this. America will eventually just give up, at which time an even angrier Iranian regime will arise.
So enlighten me, someone. Once Tehran is rubble, what's the game plan, exactly?