You are correct. In fact, one cruise line did attempt to build a ship in the USA during the early 2000s for the purpose of running cruises in Hawaii. The project was a disaster. Norwegian Cruise Lines bought the ship's carcass, towed it to Germany, and had it turned into an actual passenger vessel. They were given special dispensation to run the cruises anyway when it was finished.

https://en.wikipedia.org/wiki/Pride_of_America

You are both sort of correct. A foreign built ship can be us flagged, it just isn’t eligible for Jones act trade. I am a US Merchant Mariner who has worked on a US flagged, Australian built ship in Asia. There aware other considerations besides just cabotage laws about where one might want to flag one’s vessel.

The one thing I never understood was why everyone gets bent out of shape over shipping rules but don’t consider or care about airline cabotage.