I mean it could, but it would be pretty expensive. We know generally where ships go to fish. You watch those areas and get an idea of the various ships, you stage your ships nearby and wait. If you're really keen on being targeted you could follow ships back to port and over time have assets there wait to ID the individuals on the ship.

The problem is this would cost millions of dollars and take weeks or months unless you got very lucky. The Navy could do it in their sleep but why would they? Nobody who cares enough about this problem has the means to execute it, and nobody with the means cares.

This isn't true at all. I worked for a long time on the first implementation of the Navy's Maritime Domain Awareness System and my wife currently works for the NRO's Enterprise Collection Orchestration system that auto-tasks orbital surveillance platforms in response to automatically detected global events. Many of the capabilities are classified, but I can assure the US Navy both knows about and has some means to respond quickly (not necessarily by dispatching a manned vessel) to anything bigger than a driftwood log that appears on an Earth ocean.

The reason they don't is the Navy is not a law enforcement agency and this is not their mission.