Iran may threaten to close the Strait of Hormuz all it wants but the fact of the matter remains that it does not have the capability to do so.
Almost all of its surface combatants have been eliminated. Earlier today, the US took out 16 of its minelayers. Despite its supposed large stockpile of anti-ship and land-attack cruise missiles, almost none of them seems to have been used in this conflict, suggesting that they have been destroyed or not many were produced to begin with. Iran's air force put up less of a fight than Iraq's did back in 2003 and are essentially no longer a viable fighting force. Iran does not have any materiel with which it could credibly threaten shipping in the Strait, and certainly not with USN submarines at the standby. The US realizes this and understandably has not really paid too much attention to Iran's verbal threats.
At this point, with the Hormuz "trump card" all but negated, Iran's remaining credible deterrent in this conflict is its leftover stockpile of ballistic missiles, which is undoubtedly being depleted or destroyed at a rate faster than they could be replaced. It has no navy, air force, organized command and control, or a credible proxy network. Sooner or later, those missiles will run out as well. While it may be correct to point out certain shortcomings of the US effort in this campaign, it needs to be said that Iran faces a much more dire - and perhaps even existential - situation.