It would take much more than the forces in the region, to secure the "strait". To actually secure the strait, you have to secure the entire Persian Gulf. It doesn't matter if tankers can pass through the strait only to be blown up just of Qatar. At it's widest the Gulf is about 360 kilometers, well within the range of most drones, aerial, surface and underwater. So they would have to protect every ship in the gulf, intercept all the drones all the time, or secure the entire coastline. It's simply a task air-power and naval power can't perform. Not without major casualties and without attacks going through.

The US navies ships are good for real wars, but for casualties to be accepted, there has to be a real purpose. Escorting a bunch of privately owned oil tankers to bring down the price of gas does not really cut it.