Ships are subject to their country's rule and regulations; if a down-on-their-luck country wants to look the other way on environmental hazards or lax operating procedures on a ship, that ship can be run for cheaper than an American ship.
If we didn't have the Jones Act, we'd be hard-pressed to justify having any sort of merchant marine shipping at all -- foreign-flagged ships could undercut even moving stuff up and down the coasts or waterways.
Still, it does come up often, especially during emergencies. For example, when Puerto Rico had trouble getting goods shipped in after Hurricane Maria because there weren't enough US cargo vessels on hand to move cargo from Florida to Puerto Rico. The president at the time was criticized for not rapidly suspending the Jones Act to allow foreign ships to move critical goods.
https://www.nytimes.com/2017/09/28/us/jones-act-waived.html
https://www.brookings.edu/blog/up-front/2017/10/25/what-ever...