[hinckley buzzard]

At its narrowest point the Strait is 22 nautical miles wide. We know how this game goes from the Tanker Wars of the 80's, it doens't go very well for the bad guys. So how would sinking a single ship close the strait to shipping?

[Leaning Right]

So how would sinking a single ship close the strait to shipping?

It's all about the insurance. If a merchant ship or two is sunk, insurance rates for sailing in the area would skyrocket. Prudent ship owners would hold back their expensive ships and await further developments.

As Track9 noted, the US Navy could provide escort, but I doubt if that would make Llyods of London feel 100% confident about still insuring those merchant ships.

And yes, we could take out the launchers, but only after the missile has been fired and the merchant ship has been sunk.