What are the costs of a ground operation, and once you have the coast, does that mean US has to hold it/ guard it to keep the strait open? Thats like another forever war then. And lets say we do hold it, does that stop Iran from building nukes? Or attacking the troops on coast instead of the ships on hormuz? Is the end game a negotiation, then why not negotiate now (Iran had even offered a better deal then Obama but the idiot nepotistic lead negotiators couldn’t even understand it or were not sincere from beginng)? Or we need total capitulation and installing Reza Pehalvi, while No Kings protests are being held in US itself - what a cluster f.
I am going to group some of my answers for better presentation, so they don't answer your points sequentially
Strategic Goal level, if Trump/Netanyahu wants the strait open and to freely conduct FoN ops, then you need to hold part of the coast, or the entire coast to be able to do them, but if the Strategic Goal is to have Iranian government give up nuclear ambition and missile technology, as I said, unless the next guy in Iran cave, you will need a regime change.
As for what is the cost of a ground operation. If you are talking about a coastal operation, you are talking about anywhere from 50,000 to 70,000 troops (roughly 10 times the troop we currently had in the region, including the troop that are already in place, not just the Marine MEU or the Airborne) with supporting elements (aviation, artillery, logistics, and so on) so you are probably looking at anywhere 100,000-120,000 men, and this is what make attacking those island make sense, because it can turn them into FOB in support of a coastal operation. And you are looking at anywhere between 15-30% casualty (KIA, WIA, and MIA), harder if only us, easier if the Gulf Countries pitch in.
If we do a regime change, then you will need the Iranian opposition to support that op, you need to unite the Kurds, the Baloch, and the Shahist, which is not going to be easy, and then possibly do a full control operation like what we did in Afghanistan with the Northern Alliance, which back then it took NATO 185,000 troop, and Iran is roughly 3 times the size of Afghanistan (1.6 million sq mile vs 650,000 sq mile), so you are looking at around 500,000-600,000 troop is needed, it's not going to be doable unless we had a sort of alliance going in like we did back in 2001. And you are looking at around 2 to 3 times the casualty number, conservatively if we measure with Afghanistan.
I don't believe there is a way of negotiation, maybe time changes and people change? I don't know, but if I am Iran, I don't think I will EVER want to give up nuclear weapon from now on, and as I said, they now know they can get what they want just by holding Hormuz, unless something had change in the dynamic (like a sort of canal or pipeline) that by-pass the strait, I don't see how Iran will not use it to try to get what they want.
Whether or not Trump backs down is pointless; he can back down, but I don't think it changes anything. Even if he backs down, it wouldn't change the Iranian calculus. It basically is how soon they can resolve this now and get into the next crisis, unless and until a third option is presented to them.