But if the team is completely clueless and you need one person to take control, it helps if you know who is giving directions. You might have multiple people drawing an arrow in different directions, but because we dont know whos drawing them, we dont know whether its the team leader or someone else.
It also means the map is open to abuse, i.e scribbling, rude drawings, etc etc. But we cant see whos doing it. It means people can behave in an unacceptable manor, but they cant be caught and punished.
I suggest we just add a tiny icon next to the players name who is drawing at the time. It would flash on the party window, next to their name if their drawing. Like you see a microphone icon next to a players name when people speak on some FPS games.
Then we remove or discourage the ability to be offensive and immature! Im sure people would think twice before drawing a penis, or a Nazi symbol on the map if they know we can screen cap them doing it.
[edit]
I wrote that at 12 at night in a pitch black room, staring at a laptop. I should have added to say - only let one person write on the map at one time. Then it should be able to handle whos doing it.
Example (although the icon wouldnt be like that, it would most likely be a pen shape)...

The icon just sits opposite their name, and flashes as they draw something on the map. Very simple really. Because the lines can stay on screen for a few moment afterwards, it wouldnt let anyone else write until that vanished, and the icon would stay flashing until all the lines vanished.
That gives people enough time to screen capture any offensive images and who was doing it.
It also stops other people starting to write while any offensive material is on screen, so no mistakes are made on id'ing people.