BobR, course tracks for any military vessel in the Gulf have to be approved by Fifth Fleet. There are several factors that go into course planning in that body of water, not all of which are public. But what you described is not an option for those guys.
Of the public reasons, that would take them through Saudi waters, and the Saudi ' s don't like our vessels in there waters, and in general it's supremely bad OPSEC to transit within sight of land.
ETA: Anecdotally, Fifth Fleet micromanages navigation so bad, I have had them tell me I need to move a course leg as little as 2 miles. They don't always tell me why, either.