Good thoughts, but...
Why don't we use our registration numbers (for non documented vessels) instead of the boats name to communicate on VHF? Saying "Charlie Foxtrot 1034 Sierra Zulu" (could be abbreviated to 1034 once communications are established) would be so much more effective than "Gone Fishin" (for example). Especially for a Mayday. At least the CG could look up who the vessel belongs to and what type of boat it is, if the skipper was unable to transmit any other information.
I don't know about you, but I don't have my registration numbers memorized and by the time I fetch the registration card, my boat will have sunk.
The CG watchstanders do not have access to the state registration databases so it's much quicker to use the boat name. Also, for other boaters in the area that hear the mayday, it's usually easier to see the boat name on the side of the boat than the registration numbers. As the boat name is usually more prominent and larger.
And if they DID have access to the database, shortening it to just the numerals as you suggested, won't give them all of the information they'd need to search for the boat in the database (or even to determine which state it is registered in). Just the numerals do not indicate which state for example.
Sometimes, the boats name is so silly, the CG obviously feels silly saying it, so refers to the boat as "Vessel calling coast guard" through the entire conversation!
Yes, well, people's minds aren't usually on what they will sound like on the radio, they're usually more fascinated with their clever boat name to think ahead.
Also, when issuing Securites, the CG often gives the GPS coordinates of the navigational hazard or vessel in distress, without a landmark. If you are not near a chart this doesn't do you any good. Twice skippers responded to the CG on 16 asking what area the distressed vessel was in, only to discover that were much too far away to help. If the CG gave the Latitude and Longitude and simply added "Off Hunters Point" (for example), it would eliminate this.
Am I missing something?
If you punch in the coordinates in your GPS, it will tell you exactly where it is.