When you first group with someone, there is a pop up which offers you the option to teleport to whichever wayshrine is closest to the group leader. In the group menu, there should be the ability to offer a teleport to all group members similar to this. It would be much more convenient when traveling zones, if you choose to port into a dungeon, visiting houses, porting into a trial, etc and can help ensure that everyone is in the same instance as a convenience.
To avoid it being spammed, there could be a minute / two minute cool down or such.
PC / NA - cp 1700+ - EP magicka necro.