Agreed, but 35 miles in the Straight is not really that much sea room for a carrier battle group and the maximum depth is 90 meters (around 180 feet) for the whole gulf. Not conducive for our blue water navy, to say the least. I believe that's the big reason for the push by Rumsfeld for the Littoral combat ships.
I have direct information from friends with service experience that our submarine people really hate operating there. In fact, I've had an old hand "bubble head" make the comment that it was worse than working in close to the old Soviet Union (even within their territory) because they were afraid of being crunched by one of the super tankers in the area.
Not a good place for us to operate with our current assets. Those issue weigh heavily on our planners.
I'm sure that the traffic in that area must be harrowing for submarines. A submarine came way to close to my boat in the Strait of Juan de Fuca one day. For a while, I thought that a buoy was following us somehow, until I realized that a sub was just beneath the surface. It surfaced as it came on to our beam. I cannot remember how long my heart rate took to get back to normal. We were not near their port or in any restricted waters!
I seriously doubt that the carrier groups hang around the horn at Hormuz. We have really generous support facilities some of the Gulf states. Abu Dhabi, IIRC, can even accomodate docking a carrier.