that is unfortunately incorrect. the US Navy is indeed the strongest in the world, and over the past few decades, has been the strongest in history. It is also, however, shrinking. The worlds deadliest carrier groups are worthless if they aren't there and aren't available. Ships go on tour and rotation just as ground units do - for every ship on the sea there is one in port, one in training; which means you take our already historically small navy and you divide by 3 - that is the number of ships (of whatever power) you have to distribute, and in order for many of them to be effective at all, they have to be distributed in groups. A carrier without a carrier group to defend it is just a big target. So, the reality becomes that you don't need to have a more powerful navy to beat the US Navy... you just need to have more or even roughly equivalent power in the region, and that is becoming increasingly easy, as we decrease our presence. We are about to dip to nine carrier groups if the supercommittee fails to protect the two that will be cut if they fail - that means that we can consistently deploy three. Three carrier groups to cover the worlds' oceans. Power isn't just measured in the raw - it's measured in relation to competitors and it's measured relative at the point of impact - and once we take a look at the relative mission, geography, and local concentrations by others, the story of the Awesome Over Powering US Navy becomes very different indeed.
It's thinking like this that probably has countries like Iran and Pakistan foolishly believing they can defeat the US.
It's true that the USN plays a constant shell game with its CVBGs (Carrier Battle Groups) for the purposes you mention, but also to keep to potential enemies on their heels, wondering exactly how to defend against a constantly shifting deployment of forces. If what you "see" is not necessarily what is "available," it's difficult to plan offensives.
This model you propose relies substantially on a purely static model of US naval forces.
Fighting the USN, and by extension the US military, is like fighting a many-armed octopus. What a single country may "see" in their region, "at the point of impact," may be a single arm of the octopus. They may believe that if they can defeat that single arm, then they have defeated the entire USN (the whole octopus). Foolish! Just because other CVBGs (more arms of the octopus) aren't present
at that very moment doesn't mean that more aren't coming. You posted correctly (later) that it takes time to move ships and forces around, but they
do arrive eventually and will be ready to finish off the attacker. Defeat in a single battle does not equal victory in war. If a hot spot flares up, and other CVBGs are training or taking time off for R&R, they do not blithely continue their current activity as if nothing else in the world is happening. They cut short their training or R&R - immediately - and mobilize to support other fleet units. Other arms of the octopus, undeterred by the loss of one arm, crush the attacker.
The USN does not "need" a CVBG hovering around to cover "just Iran." Iran's naval forces are too insignificant to warrant it. CVBGs may cruise around the "Med" just to be nearby if needed. They are not there to cover a single country, but many.
I also hope that the CVBGs are not cut back. With civil unrest causing regime change all over the middle-east, now would be a terrible time for it.