The USN on the other hand has the -
Bunker Hill
Mobile Bay
Antietam
Leyte Gulf
San Jacinto
Lake Champlain
Philippine Sea
Princeton
Normandy
Monterey
Chancellorsville
Cowpens
Gettysburg
Chosin
Hue City
Shiloh
Anzio
Vicksburg
Lake Erie
Cape St. George
Vella Gulf
Port Royale
Every one of which is an actual "modern missile cruiser". Oh and also another 50 modern missile destroyers with roughly equal capability, just slightly smaller missile magazines.
Any one of which, let alone any fraction of them working together, would reduce all of Iran's surface ships to scrap at the flick of a switch. And we don't even rely on this for our main striking power. That's in the carrier and the nuclear submarines.
Get a grip people. Iran's navy is a threat to the USN like Daffy Duck is a threat to the Marine Corps.
No modern navy has entered a significant nautical engagement in over 40 years with the exception of the Falklands.
The Argentine air force managed to do quite a bit of damage with air-2-surface missles. There have been many naval studies conducted regarding closue of the Hormuz Straits, as well as the Mallaca Straits, and in every simulation blue forces take considerable losses.
I'm not suggesting the USN would not suceed. However, people need to understand the reality of the situation. These are not blue water operations. The Hormuz is extremely narrow and there are 100s of miles of coast line for silkworm batteries as well as portable fired surface to surface platforms.
In addition, our air force would need at least 1-3 weeks to establish clear approach lanes for our air assets to handle surface interdicition from the air. You do not want to bring cruisers or even frigates into such a confined area. That would be insane. I don't know if you remember the Stark incident, but this debacle shows the complexity of operating in such a tight environment and the quick decision making required for operations like this.
If you remember the Falklands campaign by the Royal Navy, you might remember that a few Argentian Mystres wewre able to breach the air cordone and do quite a bit of damage to her Majesties fleet using anti-shipping missles. When you have a sub-sonic, extremely small cylinder traveling in terms of meeters off the water, they are very hard to detect. And the warheads in these devices are extremely powerful.
One of a captains worst night mare is a small attack craft close to the shore and unvisible due to land and small craft clutter to be firing these types of weapon systems.
I can assure that any sea-2-sea engagements inside the straight would be spearheaded by subsurface systems and air. An Arleigh Burke will be hard pressed to utilize its full capabilities in such a tight cordone of operations.
An all out attempt to close the Hormuz straigts by Iran should not be brushed off ligthly. It will be a costly and potentially protracted effort that will require our political leaders to pull out a lot of stops and dispense with our reluctance to use a wide array of high tech classified technologies.