A lot of leader line snap issues could be solved if the project level yes/no parameter "Leader Line" was also embedded in or accessible in all tag families. Then we could toggle linework off or on with the leader.
For example, our room tags are a text name over a rectangle with a number in it. If I turn the leader on, it snaps to the edge of the text (sort of). If I could draw a line in the room tag family with visibility tied to the "Leader line" parameter in the project, I could underline the text room name if the leader is turned on. Then the leader wouldn't float out in space.
Better would be to create a "Leader base point" constraint or something, so users could set where the leader end snaps to.