Yeah but if they go on mission and “go dark” then you still have this starlink thing that may or may not be disabled by the person smuggling it on board. It may also be connected to official things if the owner has bad intentions, or if someone else who does finds it and co-opts it.

There is a lot that could go wrong with unauthorized radio transmission equipment on a warship, and not all of it is obvious.

Not always

Ships absolutely practice turning everything off.

Depends on where your sensors are and how much dispersion the dish has. If you are flying a surveillance plane into the "beam" then you can passively spot the ship.

You say that like Elon is personally looking at that information.

Presumably, there would be a large number of people at the company with access to that information, all of whom could be bribed or otherwise persuaded to share it.

You can’t just find a signal in the middle of the ocean.

Uh, this was the primary way the Allies defeated the U-Boats in WWII.

No they actually do go dark sometimes for exactly this reason. Of course there's always some signal source but it's the difference between lighting up like a Christmas tree and running a single IR light.