My first thought is why not a compendium that teaches teaching as well as compendium's teach firstaid or scholarship. But then that brings me back to what is the use of Teaching? I understand that Teaching allows us to teach others, but the return benefit to the teacher is small. Only at the top end does Teaching teach the skill to the teacher well.
What I would like to see a more tangible benefit to the teacher. The only thing that immediately comes to mind is increased learning of the skill being taught. I think teaching others should be a viable way of learning the skill being taught. This would be the most tangible benefit I can think of- to keep it balanced, only allow this benefit up the the ranks of teaching- so if you had 150 ranks of teaching, you couldn't learn perception from teachin if you had 175 ranks of perception, but you could learn shield at 140 ranks.
"militantly enforcing the overly rigid standards of you and your small collection of friends"