You'd instead see all domestic shipping be entirely dependant on third-party international operators paying third-world wages to third-world crews, and you'd have next to zero recourse against them if they, say, run one of their ships into a bridge, or spill a few million litres of oil.
There are a few good reasons to repeal the Jones Act (reduce shipping and trade costs in Hawaii, Alaska, and Puerto Rico) and a lot of really bad ones (the domestic shipping industry will be completely killed, and you're inviting unbounded liability from unregulated, fly-by-night international actors who don't give two craps about our laws.)
The way ocean shipping currently works is entirely incompatible with any national rule of law. Flags of convenience and corporations with non-existent liability mean that nobody in the international industry is actually following any of the rules.
The domestic industry has to follow them, which is the reason why it's not cost competitive.
The problem stemming from flags of convenience is well known and the Port State Control system [1] was created to manage it.
In other words: live up to our requirements or we will detain your vessel.
The US is not a signatory to any international port state control scheme but as is usual the US runs its own nearly equivalent scheme through the coast guard. [2]
[1]: https://en.wikipedia.org/wiki/Port_state_control
[2]: https://www.dco.uscg.mil/Our-Organization/Assistant-Commanda...
The problem is that there is too much to check, too many incentives and reasons to break the rules, and too few consequences for people who do.
You know that the Jones Act only applies to domestic shipping, right? So our ports are still full of ships dependent on third-party international operators paying third-world wages to third -world crews who occasionally run their ships into a bridge.
I'm not super sympathetic to arguments that presuppose the absolute requirement that US hegemony continue indefinitely, but certainly if you are trying to make sure your shipbuilders will be roughly as good as foreign ones or better (a reasonable policy goal, even leaving out military reasoning), cutting them off from competition with those foreign shipyards is not going to result in what you want. If there is a ready market for expensive, poor quality ships that take years longer to build than they do abroad, why would I as a shipbuilding executive invest to improve on any of those metrics? It would be wasted money, because my existing capital and workforce are already 100% utilized in high-margin activities, with orders stretching out years into the future.