Your posts are the most thought out and logical on this thread.
I tried to get a tournament going among instructors in Florida and got no response. I wasn't trying to prove anything, I just thought it would be fun and perhaps some publicity for all of us.
Many of the active instructors are my age (70) and older, and are simply past our "prime". For me, I was never a "professional" player, though I came out $$ ahead playing pool every year from 1967 to 1987 and 1990 to 2008. (brief retirement '87-'90)
While my knowledge of the game continues to increase, my physical skills have not. Health problems and economic woes have not helped.
Any kind of national or even state "Instructor Championships" would almost have to have a "senior" and "super senior" division to be fair.
How good an instructor plays is hardly as important as how well he or she teaches. And no "one size fits all"! Some folks think I'm a great instructor and others do not. That's OK...
"what is the purpose for trying to prove it?" Human ego, the curse of our species...