In which case they would use mines, ships are more easily sunk by
letting water in the bottom than by letting air in to the top. Mines
really are cheap and effective weapons.

Not necesarily. You have to lay mines. The US could blow the ship out
of the water. UAVs are mobile. You can launch them from deep inside
Iran. Also mines being static can be swept. A mobile mine (a USB) would
be quite a threat.

Note that the Iranians are as dependent on free traffic movement through
the straits as everyone else.

True, but

1) They might be prepared to hurt themselves to hurt us. In a full
scale war they wont care.

2) They will time the passage and routes of their own vessels so that
they don't get attacked.

If deterrence really did work defense policy would be a lot simpler.