Navy vessels have designated damage control parties. Naval aviators aren’t assigned to these damage control parties and most crewmen would think that they would just get in the way.
That is one thing that makes sense. Navy pilots are probably told to get to a safe place and out of the way while fire crews do their thing with the appropriate gear on.
Also; the military invests millions to train pilots. The last they want to do is lose one fighting a fire they have others there to do. It’s to protect their investment I would guess. The sad fact is enlisted personnel are not worth as much as an officer from a military perspective. It has always been this way.