Presumably, up to the modern era, captains and admirals would have exercised wide authority in situations demanding immediate action. Their superiors on land or overseas wouldn't be able to influence events after the last opportunity to dispatch orders by paper or spoken word passed. But since the development of radio, satellite, video technology, etc. it has become increasingly easy for a home authority (such as the Pentagon) to receive instantaneous updates and offer new instructions. Has this speed of information therefore decreased the authority and prestige of naval command over the years? Thank you.
Not exactly a historian, however I am actively serving Officer in the Royal New Zealand Navy.
Now in my home country, where we have a small fleet only, the positions of Captain and above (Commodore, Rear Admiral) are no longer posted to ships and are only ever shore postings to do policy or high up administrative work, and as such their prestige has decreased in non-blue water fleets that are part of multinational task forces. These days a Commander is the highest CO rank on frigates, and have the equivalent of a Captain. Our 'Admiral' is the Chief of Staff and has a more political position.
However in larger fleets the roles of Captain are still very much a seagoing position where they hold influential positions of power. While most ships' "captains" are the subordinate rank of Commander, a Captain is a more experienced Commander that will often serve as CO of a Major Fleet Unit, such as an aircraft carrier, or is put in charge of a small task group of a fleet, where the Commander has control of his particular ship, but the Captain takes charge of the task group as a whole and calls the shots with a bigger picture in mind.
However Admirals very rarely step on a ship, they're too valuable to risk losing in a war, so they're usually at HQ making fleetwide decisions removed from the scene, and use the instant communication to no longer require being in danger. Still very much a policy making rank rather than instantaneous decisions, though the most influential rank.
Like the story of the MAERSK ALABAMA (or the Captain Phillips story), the Admiral of the Task Force had to make the call to take the fatal shot, while the Captain of the USS Bainbridge was more in charge of the sailors on board.
But the story of the sinking of HMS Victoria tells us why having flag officers on board is a bad idea. Flag officers have bigger things to deal with than trying to be COs, whereas COs know their ships the best. Just like Kings stopped going to war in the 1300s, there's no advantage in an Admiral going to sea.