In my (admittedly not ship-building) experience, big problems happen when design and manufacturing are done by different organizations. The designer has to make guesses about the tools and processes at the manufacturer, and the manufacturer has little flexibility to make small changes to the design to improve manufacturability.

Of course there are ways to bridge this gap, including close collaboration and frequent back-and-forth between groups, but then when the spec has been fine-tuned for one manufacturer it can end up nearly impossible for third parties to competitively bid for a contract.

I think the navy can probably do design as well as anybody, but then they'd probably have to run the shipyards too.