That bias exists for a number of reasons, historic and political, in spite of the fact that modern missile technology makes capital ships extremely vulnerable in a hypothetical conflict against an Iran-class opponent. The small area and shallowness of the Persian Gulf amplifies the advantage enjoyed by the Iranians.
I couldn't disagree more with your assessment. The Navy does indeed have an institutional bias toward large ships, which is changing as the nature of warfare changes. Before WWII, battleships ruled. Since then until very recently, much of the focus has been power projection with carrier battle groups, which is a great way to win a cold war. Today, much more emphasis is being put on littoral and assymmetrical warfare.
However, intraservice rivalries within the Navy, the skimmers vs. bubbleheads vs. airdales budget battles, etc. have ensured that the Navy has a wide variety of surface, subsurface and airborne platforms from which to choose and is building more all the time.
The problem of keeping the oil flowing out of the middle east has been wargamed repeatedly since oil was discovered there. The Iranian "navy" has tried to close the Straits before and been unsuccessful. To say that they have any sort of advantage over the US Navy is simply laughable.