Imagine the optics of a single destroyer/cruiser being on fire. It would shatter the myth of American naval power (some are arguing that this war already did that, which I tend to agree with).

Armchair here:

Its like the issue with the Vietnam war. You need 100% perfect security, or its not worth it. If you are only 98% successful, you arent going to have oil tankers or any cargo ships even attempting it. A single failure every 2 months was a massive waste of resources.

This isn't a military decision but more a public opinion one. Should an American ship take a hit, have casualties, become disabled, etc it would put immense pressure on the administration to settle/end the war, even though on a military objective level it makes a lot of sense. This is a reality of the instant informational world we live in.

It would take far more ships (ideally destroyers and frigates ) than we can muster to the gulf.

Also, it exposes the ships to easy attack in a constrained body of water

Also, the ships would need to exit the gulf and travel a long distance to re-arm their defensive weapons, requiring even more ships.

You could hit anything going through the straight with artillery and rockets from the shore. Escort won't do much.

Too risky, and doesn't make sense from a cost-benefit perspective. Iran uses cheap and disposable weapons that are also effective. If you think about how much a single US ship costs, and the political price of US service members dying, I think the picture becomes clear.

While Iran still has fire control, these ships can be hit by shore-launched anti-shipping missiles, one way drones of even old fashioned shelling. Their "navy" was never even a factor.

Not wanting to lose USN ships as a de facto mercenary force is reason enough.