"Beside leaving them alone and let them live in peace without American influence?"
Iran has no intentions of 'living in peace' and that's the whole point.
They are concerned with overthrowing House of Saud, controlling Yemen and Bahrain, antagonizing/surrounding Israel, being a controlling force in Syria and Lebanon, and of course, making Iraq a vassal state and controlling the Gulf.
That's just for starters.
The world would be delighted for Iran to get along with it's neighbours, after all, nobody is powerful enough to do them material harm anyhow.
So you are saying that US don't want competition in the region? Because what you described: "Control of Yemen and Bahrain, being a controlling force in Syria and Lebanon and making Iraq a Vassal state and controlling the Gulf" is exactly what US is trying to do since years in the region, no?
The only special interest the US has is to hold the House of Saud stable so their Oil can be sold freely on global markets.
Other than that, they just want stability, as does everyone.
The US wouldn't even need to have ships in the Gulf if it were not for Iran. The 5th fleet is there to protect cargo from Iranian aggression.
Particularly between Egypt and Israel both for the defence of Israel and of course, that the Suez Canal stays open (open to everyone, by the way).
The US did not have anything other than a basic presence over there (5th Fleet in the Gulf) before 9/11 and that was after a major war in Iraq.
The US wants to take a 'hard position' in the ME about as they want to in South Asia. Or South America. Or Western Europe i.e. they don't. They don't really even want to be there.
Iran is super chauvinist antagonizing state - they don't simply want to 'live in peace' with their neighbours, far from it, they want to be the 'regional superpower' and take their historic position as dominating the Arabs, who they hate.
Right now, the Arab/Persian hate war is much worse than the traditional Muslim/Jewish hate war and it's causing problems.
The bulk of instability in the Middle East right now can be traced to Iran.
If Iran would just shut up and stay home, then there'd be some mopping up in Syria, Yemen might very well stabilize and then there would be peace in the ME like there has not been in centuries.
To see Saudi Arabia, UAE and Israel getting along like buddies is basically shocking to everyone who remembers how bad it was, and they are 'besties' specifically because the mutual threat they face in Iran.
So, you are kind of being cynical or very simplistic in your answer.
The fact is: regional superpower cannot compete with the world superpower, right? The Saudis have always seen themselves as the exclusive outside power in Yemen, for example. They called US when when Iranian-backed Houthi rebels marched on Yemen’s capital city and overthrew the transitional government that came into power during the Arab Spring of 2011. So it's not just about Iran, but to assure the geopolitical control in the region (through Allies and Proxy wars), control the global price of Oil, and to avoid that - in case of War - nobody does to US, what US did to Japan in the WWII (stop fuel provision)
The new episode from "Intelligence Matters"[1] talks a lot of about that. It's not just because of Iran.
It's a positive view because the US, despite it's failings, is a positive and pragmatic actor.
It's not simplistic because I'm respecting the fact that 'geostability' is a primary concern, even as that might run counter to other objectives such as democracy, free markets etc.
"regional superpower cannot compete with the world superpower" of course they can and do.
It costs the US tremendously to project it's power in Iran obviously a 'full on war' between parties would be mostly decisive in the short run but that's besides the point.
You are failing to differentiate between the kind of power that the US projects vs Iran.
The US actually supports, and helps hold together the House of Saud and therefore stability in Saudi Arabia.
They otherwise don't interfere internally. They put some pressure on Saudis for social progress but that's that.
The US is trying to help 'hold things together'.
The result of this, is that Saudi can provide oil - not to America, but to the world, at market prices.
The only special provision that comes along with US protection of the Gulf is that the Saudis cannot for example sell their Oil exclusively to China or Russia or do some kind of big strategic deal with them.
Put another way - US presence there is to stop Russia/China or some other power from taking hold.
Saudi has an interest in Yemen because it's right on the border, and full of rebels who'd like to overthrow it, ultimately, they also want peace and stability.
Iran wants to cajole, control and antagonize the Arab states and Israel and not in a nice way. They now have Iraq as a vassal state, and they'd prefer the Arabs to be their vassals as well.
If Iran did not exist, there would be almost zero ongoing fighting right now in the ME. Syria, yes, but outside of that no.
Iran has no intentions of 'living in peace' and that's the whole point.
They are concerned with overthrowing House of Saud, controlling Yemen and Bahrain, antagonizing/surrounding Israel, being a controlling force in Syria and Lebanon, and of course, making Iraq a vassal state and controlling the Gulf.
That's just for starters.
The world would be delighted for Iran to get along with it's neighbours, after all, nobody is powerful enough to do them material harm anyhow.