The Persian Gulf, despite the name, is not Iranian territorial waters. Anybody can go there. Iran would be well within its rights to send its warships into the Atlantic Ocean, yes.
US seizes Iranian cargo on even non Iranian vessels [1] with impunity. Iran sending warships would be as harshly responded to as the Cuban Missile Crisis.
It would be a minor news article that most people would not care about, just like when China/Russia sail near US territory in the Pacific (which actually does happen).
American foreign policy is fully subscribed to the idea of American exceptionalism, as are many of their citizens and media outlets. Hypocrisy means nothing to them and won’t shame them in to not doing something
This happens all the time. There is a documentary for example on the HMS Elizabeth carrier from the UK and how they deliberately navigated through Crimea waters (together with the Dutch navy) to make a point that they're allowed to do so because that water is Ukrainian and not Russian.
In the same documentary you also see Chinese ships follow around the British group, and Russian jets overflying it. All in international waters, all legal, both not appreciated by the UK side of things.
The Montreux Convention[0] prohibits large warships from transiting the Bosporous Strait. That carrier displaces 65,000 tons, the upper limit of the treaty only permits warships of 15,000 tons or less. The UK is one of the signatories to that treaty.
Ah yes, it were two ships part of the Queen Elizabeth strike group, but not the carrier itself. The command was given by the admiral that was on board the Elizabeth.
Now that you write that it makes sense why they would send only two ships and not move the group around there.
